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HEAT TRANSFER AND AGITATOR POWER REQUIREMEijTS
IN MECHANICALLY-AGITATED THERMAL PROCESSORS
WITH FIXED-CLEARANCE AGITATORS
By
WILLIAM ROY PENNEY 1,
Bachelor of Science University of Arkansas Fayetteville, Arkan~as
1959
Master of Science Univers~ty of Arkansas Fayetteville, Arkansas
1962
Submitted to the Faculty of the Graduate College of the Oklahoma State University
in'·partial fulfillment of the requirements for the Degree of
DOCTOR OF PHILOSOPHY May, 1968
HEAT TRANSFER AND AGITATOR POWER REQUIREMENTS
IN MECHANICALLY-AGITATED THERMAL PROCESSORS
WITH FIXED-CLEARANCE AGITATORS
Thesis Approved:
Dean of the Graduate College
688682 ii
OKLAHOMA STATE UNIVERSITY LIBRARY
OCT 'i.'I 1968
PREFACE
This dissertation is concerned with developing improved engineer- ·
ing design methods for thermal processors agitated by fixed-clearance
agitators.
Experiments were conducted in a 4.058 inch inside diameter by 22
inch long heat exchanger. Heat transfer coefficients, agitator power
requirements, and axial thermal diffusivity parameters were obtained
experimentally and general correlations for each were obtainedo
I am deeply grateful to my thesis adviser, Professor Kenneth J.
Bell, first for being instrumental in allowing me to do graduate work
in Chemical Engineering at Oklahoma State University, and second for
giving technical and moral support during my Ph.D. program. · I wish to
thank the other members of my Advisory Committee, Professor R. N.
Maddox, Professor J. H. Er bar and Professor J. A. Wiebelt, for their
guidance during my studies here.
I am forever indebted to .Phillips·Petroleum Company and to my
supervisor while I was employed at Phillips, Mr. W. M. Small, for the
loan of the complete experimental apparatus for my thesis work. I
I wish to thank my wife, Annette, for the support she gave while
enduring the rigors of college life with two.small daughters.
I should like to commend.Mrs. Arleen Fairchild for the 1 exceil~nt ' \
job she did typing this thesis.
I am very appreciative for having had the opportunity while at
Oklahoma State University to associate with a great group of scholars -
iii
my fellow graduate students. I shall only mention one individually:
I wish to thank Torn Rhodes for handling the mechanical details associat
ed with my dissertation after I left Stillwater.
The financial support of a two-year National Defense Education Act
Fellowship is gratefully acl:mowledged.
iv
TABLE OF CONTENTS
Chapter
I. INTRODUCTION • II • •
II. LITERATURE SURVEY .. •••e••••~•,•
III. DESCRIPTION OF EQUIPMENT. ' .
Page
1
5
26
IV.. EXPERIMENTAL METHODS . . . 34
V. EXPERIMENTAL AND CORRELATIONAL RESULTS FOR AGITATOR POWER REQUIREMENTS ............... , . 42
VI. EXPERIMENTAL AND CORRELATIONAL RESULTS FOR HEAT TRANSFER. . . . . • . . . . . . , . ,
VII. EXPERIMENTAL AND CORRELATIONAL RESULTS FOR THE EFFECT OF BACKMIXING ON THE MTD ..... .
VIII. CONCLUSIONS .i COMMENTS AND RECOMMENDATIONS. . .
A SELECTED BIBLIOGRAPHY.
NOMENCLATURE ...... .
APPENDIX A - ANALYTICAL SOLUTIONS OF THE DISPERSION MODEL
APPENDIX B - THERMOCOUPLE CALIBRATIONS ...•
APPENDIX C - TEST FLUID PHYSICAL PROPERTIES .
APPENDIX D - EXPERIMENTAL AND REDUCED DATA. .
APPENDIX E - ACCOUNTING FOR AXIAL HEAT CONDUCTION IN THE EXCHANGER WALL IN CALCULATING THE EXPERIMENTAL
57
76
92
95
99
106
. . 119
. 122
. 126
HEAT TRANSFER COEFFICIENT ......•....•... 171
v
LIST OF TABLES
Table
I. Thermocouple Calibrations . • . , . • ,
IL. Physical Proper:ties of Gulf Harmony Oil 151 •
III.
IV.
v.
Fortran Statements for Heat Transfer Data Reduction Program ••••
Fortran Statements for Agitator Power Requirement Data Reduction Program.
• 0 Cl O
Data for Heat Transfer Tests with Gulf Harmony Oil 151 and the 3 ,500 Inch Diameter Blade • • • • • 0, 0 •
VI.
VIL
VIII,
IX.
x.
XL
XII.
XIII.
Data for Heat Transfer Tests with Gulf Harmony Oil 151 and the 3,831 Inch Diameter Blade .•
Data for Heat Transfer Tests with Gulf Harmony Oil 151 and the 4.000 Inch Diameter Blade ..
Data for Heat Transfer Tests with Gulf Harmony Oil 151 and the 4.039 Inch Diameter Blade .••
Data for Heat Transfer Tests with Ethylene Glycol and the 4.000 Inch Diameter Blade •......
Data for Agitator Power Requirement Tests with the 3 . 500 Inch Diameter Blade . . . . . . . . .
Data for Agitator Power Requirement Tests with the 3,381 Inch Diameter Blade . . . . . . 0 . .
Data for Agitator Power Requirement Tests with the 4.000 Inch Diameter Blade . . . . . . . . .
Data for Agitator Power Requirement Tests with the 4,039 Inch Diameter Blade . . . 0 . . . . .
. . . . .
. . . . .
0 .
. . . . .
Page
121
125
127
129
130
140
146
153
156
159
162
164
169
XIV. Comparison of Graphical and Numerical Methods of Computing qF/qH at z = 14 Inches from the Exchanger Inlet ....• 180
vi
LIST OF FIGURES
Figure Page
1. Typical Close-Clea~ance Equipment ••• D O O O 2
2. Photograph of Eocperimental Apparatus. . . . . . . . . . . 27
3. Fluid Flow and Temperature Measurement Schematic. • • • • • • 28
4 .. Assembly Drawing of the Test Heat Eocchanger • • • 0
5.
6.
Schema.tic of Dynamometer and Tachometer ••• O O O O O
Bearing Friction for the 3.500 and 3.8.31 Inch Diameter Blades • • • • • • • • • ! • • • • • • • • • • • • 0
7. Bearing Friction for the 4.000 and 4.039 Inch Diameter Blades • , ••••••••••••
8. Agitator Power Correlation for the 3.500 Inch Diameter Blade ••••••••••••••
9. Agitator Power Correlation for the 3. 8.31 Inch Diameter Blade ••••••• , •• , •••
10 .. Agitator Power Correlation for the 4.000 Inch Diameter Blade \ • , • • • • • • . • • • • • •
11. Agitator.Power Correlation for the 4.039 Inch Diameter Blade ••• , ••••••••••
12. Correlation for Bulk Agitator Power Requirements of Flat Paddle Agitators. • • . •• , •••
Comparison of the Dependence of Pt;L on C/D for Various Data at Re = 1 O . • • • • • • • • • • • • • • •
13.
14. Typical Wall Temperature Profiles for the 3 ,500 Inch · Diameter Blade. • • • • • • • • • • • .• • • •
'
15. Typical Wall Temperature Profiles for the 3. 8.31 Inch Diameter Blade. . . . . . . . . . . . . . . .
16. Typical Wall Temperature Profiles for the 4.000 Inch Diameter Blade. . . . . . . . . . . . . . . .
vii
. . . '
. . .
• • 0 •
. . . .
. . . .
29
32
44
45
49
50
51
52
53
5-5
58
59
60
Figure
17. Typical Wall Temperature Profiles for the 4.039 Inch Diameter Blade. . . . . . • . .
HL Heat Transfer Correlation for the 3 .500 Inch Diameter Blade. . 0 . . 0 . . . . . . . . . ' . .
19. Heat Transfer Correlation for the 3. 831 Inch Dia.meter Blade. . 0 . . 0 . . . . . . . . . . .
20. Heat Transfer Correlation for the 4.000 Inch Dia.meter Blade. . . . . . • . . . . . . . .
21. Heat Transfer Correlation for the 4.039 Inch Diameter'Blade. • . • • • •••.
22. Heat Transfer Correlation ••••o••••••oe•&
23 0 Strip Chart Recorder Traces of the Millivolt Ouput of Thermocouple 12 in the Ex:changer Outlet Line for Selected Tests with the 4.039 Inch Diameter Blade .
Page
61
66
67
68
69
70
72
24, Selected Temperature Jump Ratio Data. • • . . 77
25, Temperature Ju:mp Ratios from the Dispersion Model for the Cases of (1) Constant Wall Temperature and (2) Constant Wall Heat Flux with Infinite Conduction in the Agitator 81
26, Axial Dispersion Correlation for the 3 .500 Inch Diameter Blade, . . . . . , . . . . . • . . . .
27. Axial Dispersion Correlation for the 3 . 831 Inch Diameter Blade. . ... . . . . . . . . . . . . .
28. Axial Dispersion Correlation for the 4.000 Inch Diameter Blade .•.•...•........
29, Axial Dispersion Correlation for the 4.039 Inch Diameter Blade ...•...
30. Axial Dispersion Correlation ..
31, The Effect of Axial Dispersion of Heat on the MTD from the Dispersion Model. . . . . . . . . . . ...
32. Tw vs. z for Selected Tests w:Lth the 3.500 Inch
84
85
86
87
88
89
Diameter Blade. . . . . . . ...... . • • 0 • • 174
dTw/dz vs. z for Selected Tests with the 3. 500 Inch Diameter Blade. 0 . . ·' . . . . ' . . . 0 . . 0 . 0 0 175
d~/dz vs .. z for Selected Tests with the 3.500 Inch Diameter Blade. 0 . . . 0 . . . . . . . . . . . . . 0 . . . 176
34,
viii
Figure Page
35, ct2Tw/ctz2 VS. z for Selected Tests with the 3. 500 Inch Diameter Blade. • • • . • • • . • • • • . • • • • • 177
ix
CHAPTER I
INTRODUCTION
.The industrial applications of m~cha.nically~gita.ted £11;1.id-process
ing equipment (MAFPE) a.re many and varied. The familiar unit operations
of mixing, ·chemical reaction, heat transfer and mass· trans.fer are fre-
quently effected in such equipment. H;ere we shalL be concerned only
with those process design parameters which a.re necessary to design an
agitated heat exchanger. These parameters are.:
1. Agitator power requirement
2. · Heat transfer coefficient
3. Mean temperature difference
'.l'her.e are many different types of MAFPE. This investigation is
·concerned with MAFPE which may be classified ~s !'small-clearance."
Typical "small-clearance" MAFPE are depicted schemat:j.cally in Figure 1.
11Sma.ll-cleara.nce is used. to describe the class .. of fluid .processing.
equipment.which employs agitators (anchors, scrapers, helical ribbons,
extruders, etc.) that sweep practically the entire:vessel volume.
Thus not only is the clearance between the agitator a.nd vessel 11sma.ll"
but·-also the agitator length is.approximately, equal to the vessel
length. "large-clearance" equipment employs agitators (propellers,
turbines, paddles, etc.) that sweep only·a. small fraction of the
vessel volume. .For this latter class· the clearance between agitator
. ·a.nd the vessel wall is generally large and the ··agitator length ,is
1
w T , VESSEL
L
THE ANCHOR AGITATOR THE VOTATOR
DOUBLE FLIGHTED SCREW EXTRUDER
THIN FILM EVAPORATOR SPRING LOADED SCRAPERS
Figure 1. TYPICAL CLOSE-CLEARANCE EQUIPMENT.
small compared to the vessel length.
Much of the equipment which is here called "small-clearance" has
heretofore been called "scraped-surface." This term is really a mis
nomer as almost invariably a film of liquid does exist between the
agitator and vessel wall. "Scrape:i-surface" will only be used here to
indicate the condition when the vessel wall is .scraped clean.
Small-clearance equipment employs a myriad of agitator configura
tions. From a predictive standpoint, it is convenient to classify
these configurations as either fixed-clearance or variable-clearance.
Fixed-clearance equipment employs rigid agitators . In variable-clear
ance equipment the agitators are forced toward the vessel wall by
. springs, centrifugal action, hydrodynamic action of the fluid on the
agitator and/or by the fluid friction between the agitator tip and the
vessel wall. The "slipper bearing effect" acts to hold the agitator
off the wall; thus, in general, the clearance varies with operating
conditions.
The reason for discussing all the widely different devices just
mentioned under the single classification of "small-clearance" arises
from the need to generalize design correlations. In many cases a de
sign method developed for one small-clearance device can also be used
to design other small-clearance equipment.
Objectives of this Investigation
3
The primary objective of this investigation was to develop methods
for calculating agitator power requirements, heat transfer coefficients
and mean temperature differences for Newtonian fluids in MAFPE in
which the clearance i s small and fixed. Only liquid-full systems are
4
considered.
Other investigators have conducted research aimed at these sa.me
ends. They have not been very successful. One of the major reasons
for their lack of success is that they, for the most pa.rt, have inves
tigated a particular piece of industrial apparatus. Industrial equip
ment has .two serious shortcomings .as research equipment. Industrial
equipment is generally not instrumented to measure the parameters
necessary to obtain a design method from first principles, and usually
. there are so many variables which affect equipment performance that it
is very difficult· to isolate the effect of any particular variable.
A sounder approach would be to first determine with some certainty
. the effect of the most important variable or var.iables and then use this as
a foundation for correlating the effect of variables peculiar to a
particular industrial apparatus.
With this .in mind we have chosen to restrict this investigation to
study directly only three variables: (1) the clearance between the
agitator and the vessel wall, (2) agitator spl:led, and (3) axial flow
rate.
The geometry of the experimental apparatus .was the simplest
possible - a flat knife-edged blade rotating in a cylindrical vessel.
The agitator to tube ,wall clearance could be changed by disassembling
the apparatus and adjusting the arms of the blade.
Design methods developed for this simple geometry should be at
least approximately extendable to. the more geometrically complex
industrial equipment.
CHAPTER II
LITERATURE SURVEY
In a recent publication (36)., Penney and Bell have presented a
general review and analysis of the literature on power requirements,
heat transfer coefficients and mean temperature differences for ·fluid
processing equipment employing small-clearance agitators. The most
pertinent parts of this review will be included here along with sub
sequent work and work which they did not adeq~ately cover. This inves
tigation is concerned with liquid-full systems. The literature on
thin=film systems will not be covered here.
Agitator Power Requirements.
Excellent treatises on agitator power requirements in general have
recently. been published by Bates, Fondy, and Fenic. in Chapter 3 of
reference (46) and by Chapman and Holland in reference (12). They have
swnmarized previous work on agitator power requirements. Penney and
Bell (36) swnmarized and analyzed the work on power·requirements for
small-clearance agitators. These studies will not be reiterated in toto
here. The emphasis here will be placed on correlating techniques which
appear to be fundamentally sound. Non-Newtonian work and work with a
vortex:ing free=liquid surface will not be conE1idered here.
Early workers on agitator power requirements developed a fundamen-
5
tally sound method of predicting the effect of fluid properties on
agitator power consumption. Dimensional analysis or non-dimensional
izat~on of tne Navier~tokes .equation can be used to show for an.incom-
pressible, non-vortexing, Newtonian fluid that, given geometrical
. similarity, the conventional power number ~ts ) depends only upon 2
the rotational Reynolds number ( ~i"). . This simple relationship
has been used quite successfully.to correlate power ·for agitators j,n
liquids. The form of this correlation gives us much insight into
the fluid.flow phenomena in an agitated vessel because changes in the
nature of the fluid.flow are manifested by changes in the form of this
correlation. Let us discuss the form of this correlation for a
fixed geometry -- as we go from very low Re to very hi,gh Re. Generally
below.Re= 30 the curve of P vs. Re is a stra:ight line wtth a slope of
-1; this.relationship can be obtained for an incompressible, Newtonian
.fluid by neglecting the inertia. terms in the Navie:r-Stokes equations.
Creeping flow regime is the term commonly used to describe that range
of Re where inertia forces are negligible. . Tnis .terminology shall be
used here.
In the range 30 <Re< 10, 000 the slope of P vs. Re gradually changes
from a slope of -1 to zero. :Cn this region both "viscous" and .!'inertia"
forces affect the agitator power requirement. Generally above Re= . .
10,000 the curve of P vs. Re is .essentially flat; thus., the agitator
. power requirement is independent of Re and, therefore, :independent of
·fluid viscos.ity; so the agitator power requirement is q.ependent totally
upon "inertia" forces.
Obviously from the description above the .fluid flow phenomena in.an
agitated vessel are analogous to those for fluid flow in a rough pipe
7
with the friction factor replaced by the power number. However, there
is one very important difference: In a pipe the inception of turbulence
is responsible for a rapid increase in the friction factor as Re is
increased; whereas, in an agitated vessel P changes very gradually as
-the fluid flow becomes turbulent. In.fact, P changes so ,gradually that
it is not possible to get even a rough estimate of where turbulence
starts. ·As far as.heat transfer and baclanixing a.re concerned.it is
very. important to know and desc.r.ibe · quantitatively the conditions· under
which turbulence starts and where the la.st vestiges of laminar motion
cease. For later discussion. it .is des·;i.rable here to establish criteria.
for laminar and turbulent flow in .. terms of Re. r>eveloping turbulence
has a much greater effect on heat transfer in,a.n agitated vessel than
.. it· has on the agitat0r power requirement; we may anticipate some of
the heat transfer results of this investigation at this early stage in
this· work and us.e these results. to establish criteria for the following
fluid. flow reg:i..mes : the laminar regime, · the transition regime and the
turbulent regime. · We should note here that the criterion (Re""':30) for
the creeping flow regime ·was established in .. the preceding paragraph~
If the reader will turn to the final correlation for heat transfer
for this investigation given inFigures 1.8,19,20, and 21, we shall de
fine these flow regimes. .The ordinate of these graphs is proportional
to.the heat transfer coefficient. These correlations indicate that
turbulence, which has a .significant effect on the heat transfer, starts
about Re= 150. The effect of.developing turbulence, especially,for
the small diameter blades, causes the heat transfer to:increase rapidly
with increasing Re up to about Re.= 700 where there is·a· rather sharp
break in the curve. Above· Re = 700 t·he slope of the heat transfer
correlation becomes essentially constant indicating that the random
fluctuations of' turbulent f'low overshadow any remaining traces of
periodi.c laminar motiono Based upon these observations., we shaU use
here the following criteria f'orthe various: f'low regimes: creeping
f'low·regim.e: Re<::30; laminar-regime:· Re.<150; transition regime:
150 < Re < 700; and turbulent . regime: Re ~ 700 •
8
. TI:ie f'ollowing_investigators·have used the rwidamentally sound
technique of plotting log P vs. log. Re for a particular agitatar .
geometry/ for·oorrelating power requir8Dl8llts .of snall-cleartnce agita
tors: Uhl and Voznick (48) for anchors; Nagata et ,ea. (34) for anchors., . ,. '
paddles., helical ribbons and augers; anQ. Hoogendoom and den Hartog
(20) and Gray (18) far helical .ribbons and augers. These co:rrelationa
are only correct if complete_geometricalsimilaritY. is.retained from
the experimental apparatus to the designed apparatus. Certain geome
tr:J.oal parameters may have very little effect on power but direct
experimental evidence must exist before ageometricalnriable can be
ne_glected.
other investigators have not been content to let geanetrical-vari-
ables be handled as ·parameters ·on a gm.ph of log P vs. log Re. -Tney
. have attempted to empirically correlate their effect by regression
. analysis and c~rve--fitting. 'J;'he ·following. investigators have used
this approach: Foresti and Liu (17)., Calderba.nk and Moo-Young (10)
and Beclmer and·S:mith (1) on anchors; Chapman and Holland (11) on
augers; and-;Boume and Bu.tler (8) on hellcal ribbons.
Several of the references listed.in the twe preceding paragraphs
are not sufficiently pertinent-to this investigation to.be c'i>Vered in
. lllOre detail here. In generaL.the references which w;U1 be cOJrered ~
9
more detail are those concerned with all work on anchor agitators and
.the theoretical work on screw extruders. Anchor agitators are the only
agitators.previouslytested which are sufficient:).y akin, geometrically,
to the .flat blade tested here so that data taken with them can be mean
ingfully compared with data for the flat blade. The theoretical work
on screw extruders is pertinent here because it will be helpful in
developing correlating techniques,
Foresti and Liu (17) have attempted to correlate the agitator
power requirements for a particular anchor agitator (i.e. the agitator
geometry was fixed and only fluid properties were varied) by plotting
the conventional power number (P) vs. a rotational Reynolds number
which included ratios.of geometrical parameters, '.I'his method is first
of all unnecessary because it has already been pointed out that for a
fixed geometry a plot of P vs. Re will correlate the data, and in the
second place it is unsound because a Reynolds number should be based
upon a single characteristic length.
Uhl and Voznick (48) conducted tests with anchor agitators.in a
10 inch and a 24 inch diameter vessel. The four agitators tested in
the 10 inch diameter vessel were not geometrically similar with the
three agitators tested in the 24 inch diamter vessel. Two geometrical
parameters were varied: the clearance between the agitator tip and
. the vessel wall (C) and the width of the anchor vertical arsms (wa) •
.The variation of wa had a negligible effect on the agitato:r power
consumption. Correlations of log.P vs. log Re with C/D as a parameter
were obtained for each vessel diamter. The data for the 10 inch
diameter. vessel did not coincide with the data for the 24 inch diameter
vessel, but Uhl and Voznick noted that the data could be made to coin-
10
cide if P,were :multiplied by the ratio of D to the "effective peripheral
length11 (EFL = 1 + D/4) of the agitator. They did not, however, re-
correlate the data using this suggestion. The data for the 10 inch
diameter vessel.are almost entirely in the creeping flow regime, but
the data for. the 24 inch diameter .. vessel extend well. into the transi-
tion regime (to Re= 2,000). The data for both vessels show that C
has a pronounced effect on the agitator power requirement in .. the creep-
ing flow. regime;, however, the data for the 24 inch diameter :ves,sel .;in-
dicate that Chas a.much less pronounced effect on the agitator power
requirement in. the mid'-transition regime because these data for all
three clearances almost coinc~de on the plot of log.P vs. log Re near
Re= 2,000.
Calderbank and Moo-Joung (10) have used data of Uhl and.Voznick
(48) and Foresti and Liu (17) with .their own data to develop a general
correlating method .(includi.ng'non-Newtonian behavior and all geometri
cal variables) for anchor agitatorfl. Only the Newtonian case will be
considered here. A very important correction.to this pa.per appeared
. in. a later volume of the journal in .which. it was publishe.d; the ref
erence to this correction is given.in (10) here and Bates et al. (46)
give the correction. Their corrected method.for the Newtonian case
has. a power number (P 1 ) given in equation.2-1 below, which is only a
function of the rotational Reynolds number.
(2--1)
where
n = number of blades or.arms on the agitat~r, 2 for an anchor.
ns = number of effective blade edges on the agitator, 2 for an · anchor.
L 1 L ~ = 4(D8 ) + 1/n5 .= the equivalent vertical arm height to dia-D~ e meter ratio.
De= D - Wa
L = L - w e . c
wa = width of side...arm on .the agitator.
we= width.of the bottom crossmember on an anchor·agitator.
rhe Newtonian data a.re correlated .. very well by this correlating
. method for ·wide range of Re (0.2c::::Re<4,000). However, there is a.
question about the validity of including geometrical ratios raised to
11
powers in.the power number. The data of Uhl 'and Vozhick (48) indicate
that Chas a different effect on.the agitator power requirement in the
creeping flow regime than . in . the transition re.gime; if this . be the
case, then C raised to a c;onstant power would.not represent the data
. in both the creeping flow regime and in the transition re.gime. Bates
et al. (46) have the following to say,.about this practice: "In
correlating variations in geometry, manyinYestigators have included
geometry effects as simple factors directly.in.the power number ex-
pression. This can be done as a matter·of convenience, but there is no
theoretical reason for doing so, and the practi~.e has many. poseibilities
for error." . They continue to explain .. that the most important . reason
.this practice is not sound is that a. geometrical parameter may not
have the same effect in different flow regimes.
Also the correlating method of. Calderbahk and Moo-Joung (10) does
not include the thickness of the anchor side arm .. (t) as a correlating
.. parameter. As C _. 0 the thickness of the anchor side arm would be
expected to have a very pronounced effect on the agitator power require
ment.
12
Beckner and Smith (1) have taken anchor agitator power data in a
22.9 centimeter diameter vessel with both Newtonian and non-Newtonian
fluids. Only the Newtonian case will be considered here. Several
anchors of different diameters were tested. .The data were correlated
on a plot of log P vs. log Re with C/D as a para.meter. All data were
in the creeping flow regime; therefore, for each clearance a separate
straight-line curve of slope of approximately -1 resulted. The data
were curve-fitted with the following equation:
p(fs)Yf.. -- 82 (2-2)'
l
One could define a new power number P' = P(C/D)Zj: from this
.relationship; therefore, the previous comments about the validity of
including geometrical ratios raised to constant powers in the power
number would apply to the above equation. This correlating method also
does not· include the anchor side arm thickness as a correlating para-
meter, nor, in fact does it include the length of the agitator (L),
which Calderbank and Moo-Young's (10) correlation indicates· has a
pronounced effect on the agitator power requirement.
Penney and Bell (36) have proposed a new correlating method
which considers all geometrical variables and in particular it includes
the effect of the agitator thickness (t). This method draws heavily
from previous theoretical work on screw extruders which is well
summa.:r'ized by Squires (3, 42) and Boey. (7).
The power requirements of the extruder screw are assumed to be the
sum of three processes, which are separately analyzed:
1. Power consumed between the flight edge and the extruder
barrel. (called clearance effects hereafter in this paper).
13
2. Power dissipated by viscous shear in the screw channel (call
ed bulk effects hereafter).
3. Power required to raise the fluid pressure.
Only clearance and bulk effects will be considered here since the
third effect is usually not present to any appreciable extent in other
small-clearance equipment where the agitator does not function as a
pump.
The clearance effects are calculated assuming the clearance is so
small that the barrel and flight edge approximate two fl-at p].ate1;1. One
plate of width Land infinite in length is assumed stationary; the
other plate of width Land length tis assumed to move parallel to the
infinitely long plate with a velocity equal to the peripheral velocity
of the agitator tip:?f'XdXA/ 0 End effects are neglected and the fluid
motion is assumed laminar. The gap between the plates is assumed to be
filled with a Newtonian fluid of viscosity)'<. Using the familiar
Newtonian expression relating shear stress in the fluid to the velocity
gradient in the fluid the following expression for the power dissipa
tion in the clearance is obtained for a two-blade agitator,
(2 ... 3)
Booy (7) has done the most recent work on predicting the bulk
power dissipation. He has considered screw channel curvature, whereas
previous investigators had approximated the curved channel with a
straight channel. He assumed that the channel depth is small compared
to the width. Mohr and Mallouk (3) have obtained a solution which
takes into account the effect of the clearance on the channel power.
Although all these solutions are approximate, they do give the pertinent
14
dimensionless parameters and suggest the correct functional form of
correlation. These solutions result in the following relationship for
bulk power:
(2-4)
Penney and Bell (36) have put these relationships in the follow-
ing.dimensionless.forms:
= 2;;7. {%) for clearance pow.er (2-5)
f? ::. .L f{'zi d'8 ~) hL Re c;Y; J a
for bulk power (2-6)
These relationships contain a new power number which includes d4L
rather than d5. These relationships were developed by.neglecting .
inertia forces, it shall be shown in Chapter 5 that they also hold for
turbulent flow. This has very.important consequences. This power
number correlates the effect of agitator length in all flow regimes.
Thus geometrical ratios involving the agitator length are eliminated
from consideration.
Penney and Bell (36) have recorrelated data for anchors, ribbons
and augers. They calculated that the clearance power is for all
practical purposes negligible for data in. the literature. Thus, the
power is not a function of the agitator thickness (t). The data of
Uhl and Voznick (48) indicate that agitator arm width for co:mmonly
used anchors has little effect on the agitator power requirement. With
this knowledge a plot of PtL vs. Re with C/D as a parameter correlates
the data of anchor agitators. For ribbons and augers in addition to
C/D there are three other geometrical parameters which must be con-
sidered: h/CJ d8 /D and wr/D. For agitators in common use Penney and
Bell (36) expect ds/D and wr/D will have less effect than C/D on the
agitator power requirement. They plot PtL vs. Re with C/D and h/D as
parameters •. This correlating method is fundamentally sound.
15
Bulk and clearance power requirements have not been shown experi
mentally to be independent. Also no investigator has even taken experi
mental data .which could be classified as either bulk power onlj or
clearance power only.
Heat Transfer Coefficients
Uhl in Chapter 5 of reference (46) and Chapman and Holland in:
reference (12) have presented summaries of all work on heat transfer in
agitated fluid processing equipment. Penney and Bell (36) have recent
ly su,mmarized and analyzed the work on heat transfer in small-clearance
equipment.
Huggins (21) was probably the first researcher to publish data
demonstrating that scrapers were effective in improving heat transfer
from a vessel wall to a viscous liquid but not very effective for
thin liquids. Laughlin (28) also presented early data on heat transfer
in a "scraped-surface" vessel.
Brown, Scott and Toyne (9) conducted plant tests in the turbulent
regime on two anchor agitators (1 inch and 5 inch clearance between
the outer edge of the anchor and the vessel wall) in a 5-foot diameter
, pot-type vessel. At 40 r.p.m. the 5 inch clearance anchor gave about
20 percent higher heat transfer coefficient than the 1 inch clearance
anchor. For practical correlating purposes only viscosity was varied,
however, by taking the exponent on Re from a previous work on paddles
by Chilton, Drew and Jebens (13), they proposed the following correla-
tion:
9'3 o .. 36 Re
16
(2~7)
Uhl (47) and Uhl and Voznick (48) have conducted tests on anchors
(10 inch and 24 inch diameter vessels) in the transition regime. · The .& 0./f
data are correlated on a log-log. plot of ff.Y.3 (/) . vs. Re. The follow-
ing relationships .represent .the data; a. p ~ )13 O·/&
Nu = / .. 3?- Re ?r ~ [Re~ ~~J (2-8)
The o.ata are more scattered for Re<'.'.400 than for Re>400. An interest-
ing phenomenon was discovered which did not appear·in.the final correla-
tion: An intermediate clearance gave the highest heat transfer. coeff-
icients.
Kapustin (24) has conducted tests with an anchor agitator in the
laminarregime. The suggested correlation.is;
(2 ... 10)
Considerable research effort has. been directed toward developing
design methods for the Votator. }ioulton (22) in1940 cooled hot.water
in a Votator and.published his data.. Bolanowski and Lineberry (6),in
1952 conducted tests on a number of food product~.
From 1958 to 1962 Skelland and co-workers (38,39,40) conducted a
lengthy investigation aimed at developing a general.design method for
the Votator. . Their work culminated with the following correlation;
rx.(cf )~ ((D-:t) v t° )1"°(J::f )o-b2.t6sf's(ne/'s3 (2--11).
17
For cooling vi.so ous liquids ol. = 0. 014 . and /8 = 0. 96; for cooling
thin mobile liq;uids o( = 0.039 and ;B:= o. 70. ~o criterion. is given
for. "viscous." .The functional dependence of. h.on the parameters of the
co~relation.is .as follows:
h QC (D - D ) /, () r, "·S~ (), 3 I Io. 6 Z. (!, s:, J..1 ... 4 l,O ,4
s ""s I.) A hg r< f') c (2 ... 12)
Penne~ and Bell (36) have pointed out that this. relationship is
only applicable for.the range of experimental data because h should not
approach zero as D, (D-D8) and U approach zero and that it is.most
-q.nlikely that hoc ko.04 ;in the viscous regime. .They also point out
that the dependence on. axial flow velocity predicted by eq.uation. (2-11)
probably.arose because baclanixing was ignored when the data were
reduced. ·Axial flow only affected the heat transfer coefficient in-
directly;through its effect on the mean temperature difference (M,TD).
Uhl (46) has reoently.recorrelated the Votatordata of Jioulton
(22) and Skelland (40) and the data of Buggins ~21) for scraping and
non=scraping counterrotating sweep and paddle agitator by plotting . Nt) A-i()dB
f1-V3 'f" vs. Re. The data.are correlated better j,n the turbulent
regime (Re :,,,400) than. in. the laminar regime {Re "'-400). The data in,-
d:j.cate that .the clearance between the agitator edge and.the vessel wall
has .a considerable effect on the heat transfer coefficient in the
lamir+ar regime but has little effect in the turbulent regime.
Kool (26), Harriott (19) and Iatinen: (27). have suggested that the
penetration theory should be applicable to tl:J.e prediction of heat
transfer coefficients in.tn.e Votator and similar "scraped-surface"
equipment. The heat transfer ~oefficient from the penetration theory
is as follows:
(2-13)
latinen (27) has put this relation in the following dimensionless form
for a two.;..bladed agitator:
Nv = (2 ... 14)
latinen (27) checked the penetration theory with .the data of
. Houlton (22) and Skelland (38). The data of Houlton checked well .. ,but
those of Skelland did not. The data of Houlton were in the turbulent
regime (Re ;;:,700) and those of Skelland in the transition regime (150 <.
Re-::::700). latinen concluded that the heat transfer mechanism in the
transition regime must be very different from that implied by assump-
tionp of. the penetration.theory. The effects of axial dispersion un-
douotly confounded the check of Skelland 1s data. Harriott (19) took
data on carrot puree and oil in a Votator and checked these data, along
with Houlton 1s (22) data, with the penetration theory. The penetration
theory predicted coefficients up to 50 percent too high for the puree
and oil. Harriott (19) suggested that the penetration theory may. have
predicted high coefficients because the viscous fluids did not return
. to the heat transfer at their bulk temperature.
Penney and Bell (36) have. noted that the penetration theory only
agrees with experimental data for the Votator in the turbulent regime,
but they go on to point out that the penetration theory predicts that
the heat transfer coefficient is independent of fluid viscosity (which
it is in the creeping flow regime); whereas, it is: known from many
previous experiments that the heat transfer coefficient is significantly
dependent upon fluid viscosity in the turbulent regime. They/thus
conclµde that the penetration.theory is .not applicable to the prediction
19
.of heat transfer coefficients in agitated heat exchangers •
. The Votator blades do not wipe the wall of fluid. .The hydro-
dynamic lift force keeps the blade off the wall resulting.in a. residual
liquid film after the wiper passes. This residual film would be
expected to affect heat transfer. Kool (26) and Jepson (23).have
suggested that this film might be considered for predictive purposes as
a solid layer on.the exchanger wall. They both show graphically how a
stagnant film of liquid would affect the heat transfer coefficient
predicted by the penetration theory. Bell (2) noted that the stagnant
film-penetration theory model could·be approximately expressed in
closed form as
I h = (2-15)
'.I'his relationship can also be expressed in the following dimension;,..
less form:
I I (2 ... 16)
/," 7 Rep,..
Penney (3?) has .checked·this model with laminar flow data from a
constant clearance device called the Spiralator. For large clearances,
theory and experiment agreed well but for clearances approaching zero
this model predicted coefficients 100 percent too high •. This check is
only qualitative because the effect of axial flow on the heat transfer
coefficient could not be separated from the overall effect of axial
flow plus agitator rotation. Clearly.this model is in error for small
clearance because the axial flow would, if anything, increase the
coefficient above that existing at zero flow.
20
From a practical design standpoint, the correlation of Uhl and · i/__v D~g
Voznick (48), which correlates p,,."f3 (/) vs. Re, is the only design
me.thod which one could use with any degree of confidence. In the
turbulent regime this method is. probably adequate to predict the heat
transfer coefficient but in the laminar regime there appears .to be an
effect of clearance which has not yet been.determined.
The Effect of ~ial Dispersion of Heat
on the.Mean Temperature Difference
Before examining.specific literature it seems worthwhile to make
some general comments concerning the effect of axial dispersion of
.. heat on. the mean temperature difference in heat exchangers. In an
agitated heat exchanger there arethree possible mechanisms for the
axial dispersion of heat:
1. axial molecular conduction in.the fluid stream
2. axial conduction in. the conduit wall and a.gitator
3. "'bac.kmixing", i.e., ccmvective transport of heat which
tends to level out the axial t.emperature, (e.g. Taylor
vortices and fully developed.turbulence).·
Effects (1) and (2) have not been investigated, but there is
a volwm.nous literature pertaining to backmix.ing. Much of it is only
:of marginal concern to this.investigation, and only.that most pertinent
to this investigation will. be covered here. Recent rev~ew articles by
Li ,(30), Bischoff (4), Klinkenberg (25) and Oldshue(35). have' covered
the general field.
There are really three rather distinct.problems associated with
. developing.· a design method for the effect of backmixing on the mean
21
o,
mean temperatu:re difference (MTD). The first problem is to develop a
mathematical. model for the backmi.xing phenomenon. .The second problem
is to develop experimental techniques to measure the backmixing para-
meters of the mathematical model. The third problem is to correlate
the backmi.xing. parameters with the operating . parameters of the heat
exchanger.
Historically there have been two approaches to developing ma.the-
ma.tical models for backmixing - the "dispersion model" and the
"equivalent completely mixed stage" concept which has been advanced by
Young (50) and others. The dispersion mQdel is equivalent to Fick's
law of diffusion or Fourier's·. law of heat transfer with the molecular
transport coefficient replaced by an effective transport coefficient
(oC~) due to the backmi.xing. Thus the dispersion model is a one para~
meter model, namely (o<..;;. The "equivalent completely mixed stage"
concept views the backmixing.in. terms of the number of completelymixed
stages which will give the same performance as the real process; it
has not proven very useful because it has not been possible to obtain
general correlations of the equivalent number of stages in terms of
. the operating parameters. Only the dispersion model will be discussed
further.
The first solution of.the dispersion model of interest here was
given by Danckwerts (15) in 1953. He solved for the effect of back-
mixing on a first order chemical reaction in a tubular reactor with no
axial dispersion in. the inlet and outlet lines. Wehner and Wilhelm
(49) have generalized Danckwerts 1 solution to include dispersion in
the inlet and outlet lines. Their theoretical results predict that
dispersion in the inlet and outlet lines does not change the theoretical
22
solution for the reactor. These solutions are exactly the same as the
solutions for the fluid temperature distribution in a heat exchanger
with constant wall temperature •. They are recast in heat transfer terms
in Appendix A for sake of completeness here •. The final solution for
fluid temperature vs. axial distance in the heat exchanger is given
below:
a :.
# ---~
(1-1-'a) z. e Q {~
/ 1-1- ~~
h/1 We
VL ale
z -t:1~ r1-4) e ~
(2-17)
(2-18)
(2-19)
(2-20)
(2-21)
Note that the temperature at any location is a function of only two
· dimensionless parameters: · ft and: Pe. .The solution above is also
applicable to extraction when the concentration in one phase can be
assumed constant. For two parallel flow streams in. intimate contact
and transferring heat or mass, the solution to the dispersion model
is given_by..Sleicher (41), Miyauchi (33:) and Miyauchi and Vermeulen
(32). As far as. this. investigation is concerned, the above papers
have solved.the first problem !Ilentioned above, namely, developing a
.mathematical model for the baclanixing phenomenon.
Miyauchi and Vermeulen (32) also shed some light on the second
problem of developing experimental techniques to determine the dis
persion parameters (for our case Pe). For the case of constant wall
temperature they have shown that only the temperature jump ratio To-~ .
( .,- -r..· ) and ,12 have to be measured in order · to determine Pe. The
23
/,t. - /t: I-' .
relationship between ~ - ;¥. , /? and Pe is derived from the appropri-L - Ir
ate solutions to the dispersion model in Appendix A:
To-?;.· -- 
There are two recent references in which axial dispersion was
measured with are pertinent to this investigation. Mixon, Whitaker
and Orcutt (31) have used the transient delta-function pulse input
method (with a radioactive tracer) to measure ffee. in a liquid-liquid
spray tower heat exchanger (water as the continuous phase and a light
24
oil as the discontinuous phase). They also analyzed earlier oil-water
spray tower data and obtainedO(e from measurements which were taken using
both the steady state method and the transient method. For equivalent
operating conditions o<...~(obtained from both steady state and transient
tests) and 5Je were found to be approximately equal.
Croockewit, Honig and Kramers (14) have measured the effective
diffusivity of mass.in an annulus with the inner cylinder rotating by
measuri_ng the response of a sinusoidal tracer input. They have obtained
a correlation for in terms of the system parameters. This correlation
and the conclusions to be drawn from it will be discussed in the next
paragraph. Their mechanical system differed from the system used here
only in the agitator. This is the only system found in the literature
which might be expected to obey the same general correlation as the
system of this investigation.
Now we move to the third and last problem mentioned previously,
namely, correlating backmixing with the operating parameters of the system.
Taylor (43 ,44) was the first investigator to tackle this problem the.ore-
tically. He solved the axial dispersion problem for completely laminar
and completely turbulent flow in tubes. He showed that the dimensionless
( <=><u•r,. ) ( ~1= dispersion parameter ... was a function of Re and Sc in fact uC rv
ReSc) in.the laminar regime and a function only of Re in the turbulent
regime. Levenspiel (29) presents these relationships in
graphical form and shows the typical range of experi-
25
mental data. later investigators have for the most part used equival-
ent correlating methods. In general a dimensionless dispersion para-
meter is correlated as.a function of the pertinent dimensionless fluid
dynamical parameters of the system. For an agitated heat exchanger in
the.turbulent regime one would expect that the dispersion number might
be correlated with the geometrical parameters, the rotational Reynolds
number and the axial flow Reynolds number. Croockewit, Honig and
Kra~ers (14) have done just this. For the annulus with the inner
cylinder rotating ,?J)E . /y'(O-d)d
they plotted ;.,;(p-d)d vs. 2 v and found that
all data fell essentially on the same curve. Thus neither a change in
axial flow.rate (axial Reynolds number) or a change in inner cylinder
d . t ( t ) ff t d th 1 t· h. · b t frffee d iame er geome ry a ec e ere a ions 1p e ween /./(.0-d)ci an ;,;(p-d)d
ZP Penneyand Bell (36) have pointed out that there is no method to
predict the effect of backmixing on the M'rD in heat exchangers. In
.fact, no investigator of. heat transfer inag:l..tated heat exchangers,
except a recent investigation by Uhl and Root (45) on heat transfer
to agitated particulate solids, has even considered that backmixing
could affect equipment performance. In.some investigations, the effect
of backmixing has been mistaken for the effect of axial flow rate.
CHAPTER III
DESCRIPTION OF EQUIPMENT
A photograph and a schema.tic diagram of the test apparatus are
presented as Figures 2 and 3 respectively.
The apparatus is composed of the following major items:
1. The test heat exchanger
2. The A.C. auto transformer -and the nichrome heating element
3. The D.O. motor which rotates the agitator
4. The test fluid reservoir
5. The test fluid circulating pump.
Test Heat Exchanger
Figure 4 is an assembly drawing of the test exchanger. The shell
of the exchanger was a 4.058 inch inside diameter and 4.46 inch out
side diameter aluminum cylinder. The ends of the exchanger were· con
structed from 3/4 inch thick Plexiglass sheet. The aluminum agitator
was a flat· knife-edged blade so designed that the clearance between
the agitator blade tip and the exchanger shell wall could be varied.
The exchanger wall temperature was measured in eleven locations
(2 inches apar.t and 1 inch from either end) with 30 gauge, teflon
coated, iron-constantan thermocomples. The thermocouple junctions were
made with mercury bath thermocouple welder. The thermocouples were
inserted into holes drilled almost tangentially into the exchanger wall
26
I ,, .. .• w T
..............•. , ..•.•.....•.. ... ··~ ··~ •.•.......... .... ; • ; ' .~, -----·- ··
Figure 20 · Photograph of Experimental Apparatus
27
3/4 HP D-C VARI AB LE
SPEED MOTOR
NOTE: THE BEAD.OF ~WAS PLACED IN
THE CENTER OF A - 114 DIA. ORFICE ·IN
THE PUMP OUTLET NIPPLE.
TEST HEAT EXCHANGER
NOTE: ALL FLOW LINES ARE l IN CH I. D. TYGON TUBING
BYPASS LINE
GEAR PUMP VIKING GX-'151 NOMINAL 5 GPM
FLUID RESERVOIR AND VOLUMETRIC FLOW METER
PARTITION
SPRINGLOADED GATE
Figure 3. FLUID FLOW AND TEMPERATURE MEASUREMENT SCHEMATIC. 1\) CQ.
PLEX I GLASS ENDPLATE - t x st- x st
I
4460~ I 4.058 D. • .001~~=-~,,
. / ~ ,, / '
~/ \ @) I I
11 l'k '- '\I f - : I
@) \ \
$\2...WALL \ ~2
"-', '~~/ --HEATING ELEMENT BINDING LUGS ! -t- D. x + LONG COPPER LUGS WHICH
WERE USED TO CONNECT THE ELECtRICAL
rl H EATI NG TAPE TO THE A- C illCTRICAL LEAD
-n I 11
l! i !! .
SLOT FOR THERMOCOUPLE WIRES .064x.064.
HOLE FOR THERMOCOUPLE · .040 D. x -t DEEP
ELEVEN THERMOCOUPLES - 2 INCHES APART
WITH FIRST AND LAST I I NCH FROM ENDS.
I.it: .. ",.\r> ~j:~§=§~§~§:::::::;::§=s;=-, ~i
~ . . W-1-,~il' i6 i
. 16
BEARING- l.00 0.0., .502::g~ I.D., .63 LONG;
.065 x T VITON 0-RING SHAFT SEAL
MATERIALS OF CONSTRUCTION
EXCHANGER SHELL: 6063~T6 AL.SCHEDULE 40, 4" PIPE
AGITATOR: SOFT AL.
DRIVE SHAFTS: STAINLESS STEEL
Figure 4. ASSEMBLY DRAWING OF THE TEST HEAT EXCHANGER.
I\)
'°
as shown in Figure 4. The thermocouple leads were brought out in a
groove in the exchanger wall. The leads were covered in the groove
with a strip of sheet aluminum which was peened into the groove so.
that it was flush with the outside of the wall. The thermocouple
junctions in the drilled holes were approximately 1/16 inch from the
inside wall.
Thermocouples sheathed in stainless steel were inserted through
the endplates in order to measure the temperature just inside the
exchanger inlet and just inside the exchanger outlet. Slots in the
agitator prevented these thermocouples from striking the rotating
agitator.
The fluid temperature just outside the exchanger at the outlet
was measured by.inserting teflon-covered thermocouples into the ex-.
".30
changer outlet port. The thermocouple wires were led out between.the
Tygon outlet line and the Plexiglass port.
The shaft bearings were made of Fluorosint. Viton 0-rings were
used as shaft seals.
The exchanger was electrically heated over the entire length by
Chromel A heating tape (0.002 inch thick, i inch wide, 0.531 ohms
per foot). The heating tape was wrapped over teflon-tape electrical
insulation. The gap between successive windings of the tape was approx-
ima. tely 1/32 inch. The electrical power to the tape was supplied
through. a 220 volt, 20 'ampere Powerstat.
Motor, Dynamometer and Tachometer
The agitator was driven by a 3/4 hp DC motor (manufactured by
Century Electric). The motor speed was varied between Q-1200 rev./min. r-:.·
by an ACF Electronics Model 430 Motor Control.
The motor was cradle-mounted as depicted ;in Figure 5 so that
torque could be measured. The torque was meas~red by weights which
were slid along an arm attached to the motor frame until the torque
produced by the weight equaled the motor torque.
The motor speed was measured by timing an integral number of
revolutions of an idler which was belt-driven from the motor-shaft.
31
As the idler rotated it actuated a roller microswitch once per revolu
tion. This switch in turn caused an electric counter to advance one
digit per revolution. Timing was done with a standard Electric Time
Co. electric timer (smallest graduation on face 1/100 second). The
electric counter was connected to the timer switch so that the timer
and counter were started and stopped simultaneously.
Pump and By-Pass Valve
The pump was a Viking GX-151 gear type (nominal 5 GPM), It was
belt driven at approximately 400 rpm by a! hp, 1725 rpm, A.C. motor.
The flow rate through the exchanger was controlled with a 3/4 inch gate
valve.
Reservoir, Flow Meter and Cooling Coils
The reservoir was constructed of! inch thick Plexiglass sheet.
It was partitioned along a vertical centerline into two 8 x 8 x 18
·inch compartments. The pump suction line and the bypass line termi
nated in the other compartment. A spring~loaded, liquid-tight gate
was built into the center partition. The volume flow rate of the
liquid through the exchanger was obtained by closing this gate and
A
WEIGHT: No. I -.227 THICK, 241.5 GRAMS No. 2 ~.375 THICK, 465.5 GRAMS No .. 3 -.514 THICK, 557.0 GRAMS
WEIGHT ARM: to. x 18 LONG ALUMINUM
IDLER: BALL BEARINGS RATIO OF DIA. OF IDLER TO DIA. OF SHAFT= 6.11 . l===~==:;z:::3 ...._ __________ __.
SCALE SUPPORT
ROLLER-ARM MICROSWITCH: OPERATES I I 5V A-C COUNTER ONCE PER REVOLUTION OF I OLER
MOTOR SUPPORT RING: MILD STEEL
WEIGHT ARM RETAINER
VIEW A-A
Figure 5. SCHEMATIC OF DYNANOMETER AND TACHOMETER
32
then measuring the time required for the liquid to rise a measured
distance up the wall of the compartment in which the exchanger outlet
line terminated.
Cooling coils were placed in both compartments of the reservoir.
Each contained approximately 50 feet of i inch copper tubing wound
into two concentric coils of approximately 6: inches and 4 inches
diameter. City water was used for cooling.
Electrical Power Measurements
The voltage drop across the electrical heating tape was measured
vdth a Weston Model 433 A.C. voltmeter which has three scales: 0 to
150 volts, 0 to 300 volts, and Oto 600 volts. The Oto 150 volt
scale was always used. The guaranteed accuracy was ±'3/4 percent of
the full scale reading.
The electrical current through the electri·cal heating tape was
measured with a Weston Model 433 A.C. ammeter which has three scales:
O to 5 amperes:; 0 to 10 amperes and O to 50 amperes. The O to 5
ampere and Oto 10 ampere scales were used. The guaranteed accuracy
was ±3/4 percent of full scale reading.
33
CHAPTER IV
EXPERIMENTAL METHODS
Temperature Measurements
The 15 thermocouples indicated on Figure 3 were calibrated in an
oil bath which was controlled to± 0.02 F. These calibrations are
given in Appendix B. In general the teflon=covered couples agreed
with the thermocouple tables within± 0.1 F and the stainless-steel
sheathed couples were 0.8 F ± 0.1 Flower than the reference table
valves over the calibration range of 100=200 F.
The experimental measurements were taken with a Leeds and North
rup Model 86~ Volt Potentiometer with the reference junction in an
ice bath.
Considering both calibration and potentiometer errors, the temper=
ature measurements should be accurate to within 0.2 Fa The wall
temperature measurements should have this accuracy. Unfortunately the
mixing cup temperatures are not this accurate because the floVITing
streams were not always radially isothermal. Additional thermocouples
were installed in the inlet and outlet lines to determine if radial
temperature gradients were present. One additional thermocouple was
installed near thermocouple 13 in the inlet line. During all sub=
sequent testing the agreement between the two thermoucouples in the
inlet line was almost always within Ool F indicating that the fluid
as it left the pump was essentially isothermal. Two additional thermo-
34
couples were installed! inch above and! inch below thermocouple 12
in the outlet line. At low Re (below 300) the variation in readings
between the three thermoucouples was as much as 5 F; however, above
Re= 300 the agreement was generally within 0.5 F. A seemingly
35
plausible explanation for this behavior is that the turbulence at
higher Re causes the stream to be nearly isothermal in the outlet line.
For Re<: 300 the outlet temperature was determined from a heat balance.
Heat Loss to the Atmosphere
The exchanger was insulated with fiberglass insulation about 5
inches thick. Heat loss was measured at three heat rates. The
specific heat loss (Q/(Tw - Ta)) increased as the exchanger wall to
ambient temperature difference increased. The experimental values of
Q/(Tw - Ta) were 0.5, 0.64 and 0.71 Btu/hr Fat (Tw - Ta)= 23, 80 and
120 F respectively.
Liquid Volume Flow Rate
The liquid flow rate was measured by closing .the gate in the
reservoir partition and then measuring the time for the liquid to
rise a measured distance.
This method was found to give rise times reproducible to within
2 percent. The reservoir is estimated to be 8 x 8 inches to within
1/16 inch on a side. This would give a potnetial error in area of 2
percent. The volume flow rate should then be accurate to± 4 percent.
Power Measurements
The weights were measured to a precision of 0.5 grams. The
distance of the weight from the center of rotation was measured on an
18 .inch scale. The accuracy of the distance measurement is estimated
to be 1/16 inch.
36
The friction in the exchanger bearings was a significant portion
of the total power input to the agitator in many cases. For the 3.500
inch agitator at low torque the bearing friction was as much as 25
percent of the total power. For higher torques, the bearing friction
was a much smaller portion of the total power - about 3 percent at the
highest torques for the 3.500 inch paddle and less than 2 percent for
the 4.039 inch paddle.
The bearing friction was measured with the exchanger empty. Under
normal operating conditions with a liquid-full exchanger the bearings
were lubricated by the test liquid (see Figure 4); however, to measure
bearing friction the exchanger had to be drained; therefore, only the
fluid which did not drain from the bearing was left to lubricate.
Measurements were made in rapid succession going from low speed to
high speed in order to minimize the effect of the residual oil in
the bearings becoming hot and therefore less viscous. These measure
ments were not under the same conditions as during testing because
the exchanger contained no oil.
The bearing friction measurements are explained and the data are
given in Chapter 5. The curve-fits for computer reduction of the data
are also given.
The 0-rings were originally placed very near the edge of the
Fluorsint bearings. The lip holding the 0-rings in place broke off
one of the bearings and then a new 0-ring groove w~s cut in the center
of the bearings. The bearing friction changed because the new 0-ring
37
groove was not the same dimension as the old o~ring groove. There was
also an error in power because of friction in the roller bearings on
which the motor was balanced. This erro:r;_which was undoubtedly
negligibl~_was also relatively greater at low torques than at high
torques.
It is rather difficult to estimate the magnitude of errors in the
measurement of agitator power requirements because most of the error
was a result of bearing friction and the bearing friction measurements
could not be ma.de under operating conditions. Probably the best esti-
' mate of both systematic and random errors in the agitator power measure-
ments can be obtained by inspecting the data in final correlation form
in Figures 8, 9, 10, and 11. Errors in bearing friction result in
systematic errors in the agitator power requirement calculated from
the experimental data and these systematic errors in turn show up as
systematic errors in the conventional power number (P). The errors
are manifested on the correlations most generally by a gradual de:via.-
tion of the data for a particular series of runs from the reconnnended
curve at low torques (i.e., low Re). Little would be gained by listing
here maximum deviations from the reconunended curyes as one can ascertain
this and much more by" inspecting the final correlations.
Adjustment and Measurement of the Blade to Tube Wall Clearance
The blade diameter was set as desired by use of a cradle. The
cradle consisted of two semi-circular wire supports which supported
the shafts attached to the blade. When the blade was: mounted on its
cradle it could be rotated freely and the shafts had very little
lateral movement. The cradle was used to assure that the clearance
38
would be the same on both sides of the blade. As the blade was hand-
rotated in the cradle a smooth surface was held so that each side of
the blade just touched the surface as it moved pa.st. The diameter of
the blade was usually measured in five locations along its length; the
4.000 inch blade was measured in six locations. The maximum deviations
between these measured diameters for each blade are as follows: J.500
inch blade, 0.0008 inches; 3.8.31 inch blade, 0.035* inches; 4.000 inch
blade, 0. 010 inches; 4. 03 9 inch blade, 0 _. 006 inches •
Operating Procedure
Tests were conducted with and without heat transfer through the
exchanger wall. All experimental variables were measured q,uring heat
· transfer tests. From these measurements agitator power requirements,
heat transfer coefficients and axial heat dispersion parameters were
determined. Only agitator power requirements were obtained during
tests without heat trans.fer. The operating procedure for the heat
transfer tests will be explained first.
To start a series of heat transfer tests the agitator was started.
and set at an intermediate speed and the electrical power to the wall
heating element was turned on. The cooling water was not immediately
turned on. The test fluid was allowed to heat to a desired temperature
and then the cooling water was turned on and adjusted by means of a
needle valve in the cooling water line until the desired temperature .
1!-'ftlis deviation is larger than the others because the agitator diameter was adjusted with th!=) aid of a 6 inch metal. scale rather than a micrometer. Use of the scale rather than the micrometer was necessary because the Engineering Sho~ from which the micrometer .was borrowed was closed when the blade diameter was changed. The. 3.8.31 inch blade diameter was measured with the micrometer after it was tested.
39
was maintained. It usually took from one to two hours to obtain quasi
st.eady-state operation. Completely steady-state operation could not be
attained because the cooling water temperature and the electrical power
to the heating element varied in an apparently random fashion. These
variations were so small, however, as to not significantly affect the
accuracy of the experimental measurements.
Once this quasi-steady-state was reached, a series of tests were
conducted by incrementally varying the agitator speed~ For a single
test series runs were' made at about 10 to 20.agitator speeds; this
usually required 2 to 5 hours. At every agitator speed the following
experimental values were recorded in the order given: 15 temperature
readings in the numerical order given in Figure 3; voltage drop across
exchanger heating element; current through exchanger heating element;
the initial cycle timer setting; the time the cycle timer was engaged;
the final cycle timer setting; the time for the test fluid to rise 6
inches in the reservoir; the potentiometer setting on the D.C. motor
control; the lever arm of the dynamometer weight; and the number of
the weight (or weights) on the dynamometer lever arm. It usually took
3 minutes to complete the readings for a single test.
When the agitator speed was changed from test to test the agitator
power requirement and the heat transfer coefficient changed. Thus the
test fluid bulk temperature and the exchanger wall temperature also
changed. After changing the agitator speed, a wall temperature thermo
couple (usually thermocouple 6) and the outlet line thermocouple were
monitored visually on the spotlight galvanometer in the potentiometer.
When these temperatures were so steady that no change could be detected
over a period of 2 to 3 minutes or when their dynaµd.c behavior was
40
obviously being influenced primarily by the random fluctuations in line
voltage and/or cooling temperature, then the experimental readings were
recordedo Generally it took from 10 to 30 minutes to reach lined-out
operationo The time between successive tests can be ascertained from
the computer printouts of the experimental and reduced data in Appendix
D; Central Standard (or Daylight in season) time in minutes was used as
test identification.
Successive tests were usually but not always conducted by going
to the next higher or lower agitator speed. For many tests {especially
in the laminar regime at low agitator speeds) the procedure was to
increase and decrease (or vice versa) agitator speed for successive
tests. This was done in order to eliminate possible hysteresis effects
of developrmg, turbulent flow. Duplicate tests were also quite frequent
ly conducted; these are readily identified from the experimental and
reduced data in Appendix D.
Only agitator power requirements were measured during tests with
out wall heat transfero The temperature of the test fluid was always
below room temperature; it was adjusted to the desired value by cooling
the test fluid in the reservoir with city water flowing through the
reservoir cooling coils. In a few tests the city water was cooled be
low its normal seasonal temperature by passing it through a copper tube
coil immersed in ice water prior to flowing through the reservoir cool
ing coils.
Once the test fluid temperature was adjusted to the desired value,
the test fluid was circulated through the heat exchanger until the heat
exchanger had reached approximately the temperature of the test fluido
Then a series of agitator power requirement tests were conducted by in-
41
crementally varying the agitator speed. At every agitator speed the
following experimental readings were recorded in the order indicated:
the number of the weight (or weights) on the dynamometer lever arm;
the lever arm of the dynamometer weight; the wall temperature at the
center of the exchanger (thermocouple 6); the temperature just~.inside
the exchanger inlet (thermocouple 14); the temperature just inside the
exchanger outlet (thermocuople 15); the initial cycle timer setting;
the time the cycle timer was engaged; and the final cycle timer setting.
Successive tests were conducted as fast as the readings could be
taken in order to minimize heatup of the test fluid by the viscous
dissipation from the rotating agitator. The time between successive
readings was approximately one to two minutes.
Selected experimental and reduced data are given in Appendix D.
CHAPTERV
EX:PERIMENTAL AND CORRELATIONAL RESULTS
FOR AGITATOR POWER REQUIREMENTS
Ex:perimental and Reduced Data
Agitator power requirement data were taken during the heat transfer
tests and during the tests without heat transfer. The experimental
variables which were monitored are given in Chapter IV in the section
entitled "Operating Procedure."
The data were reduced on the 7040 digital computer. Two FORTRAN
programs were used in the data reduction. One was used for the heat
transfer tests and the other was used for the agitator power require
ment tests. FORTRAN listings for both these programs along with ex
perimental and selected reduced data are given in Appendix. D.
In order to reduce the agitator power requirement data to corre
lational form by computer, the following curve-fits were obtained:
temperature vs. millivolts from the iron-constantan thermocouple tables;
fluid physical properties vs. temperature; and bearing friction vs.
agitator speed. Appendix. C documents the data on fluid physical pro~er
ties for Gulf Harmony Oil 151, the only test fluid used for agitator
power requirement tests. The curve-fit of the thermocouple tables is
documented in the computer programs.
L.2
43
Bearing Friction
The accuracy of the agitator power requirement at low blade speed
was affected significantly by bearing friction. The bearing friction
was measured under dry conditions (i.e. the exchanger was empty of
test liquid). This condition would not be expected to give the same •-.' .. ·--:>'
bearing friction as normal liquid .... full test conditions; however, ~·e
bearing friction could not be measured with liquid in the exchanger.
It is not possible to determine experimentally how much the measured
bearing friction deviates from that encountered in actual testing. It
is most likely, however, that the measured bearing friction is greater
than the actual bearing friction because the bearing friation tests
were conducted with the exchanger initially at room temperature with
the exchanger drained of test fluid. These tests were conducted very
quickly (usually less than 5: minutes for a particular blade diameter)
so the re1;1idual oil in the bear:i,ng would not heat very m-q.ch.
The bearing friction measurements are presented in the graphical
form of bearing friction torque vs. agitator speed in Figures 6 and 7
for the four blades tested. You will note from these curves that the
bearing friction is not constant from blade to blade nor is it constant
for a particular blade as will be noted by inspecting the bearing
friction measurements for the 3.500 inch diameter blade. Ea.ch time
the agitator wa1;1 removed from the exchanger and reinserted the bearing
friction was likely to change. There are several reasons for this; a
few of the most important will be mentioned briefly: In inserting the
shafts on the agitator through the 0-ring seals the 0-ring could
possibly rotate in its seat or it might be damaged by the shaft being
forced through it; the agitator shafts could have been forced out of
1.2 r---r--;===F=====i~===1====+===::::r:==-
o.a
,...... ~ o.4 l:l ;j 0 P.
I
.r:: C) i:::
,:'.; 0.2
~ S. 0
E-1
i::: 0
~ 1.0 C)
•rl
rt ~
•rl
~ & o.a
o.6
o.4
0
Q
Curve-fit for computer
200
0
Curve-fit for computer
BEARING FRICTION FOR J.500 INCH DIAMETER BLADE
O Bearing friction for all tests with the J.500 inch diameter blade up until JO May 1967 when the 0-ring in the inlet end of the exchanger malfunctioned.
O Bearing friction after new 0-ring installed and until the 4.039 inch diameter blade was installe4.
0
Curve~fit for computer
BEARING FRICTION FOR J.831 INCH DIAMETER BLADE
00 00
Agitator Spe.ed (revolutions/minute)
Figure 6. Bearing Friction for the 3.500 and 3.831 inch diameter Blades
44
1.2,...--------,r----------,r----------,~-------.--------.._--------------..
0
o.a
0
Curve-fit .for computer
BEARING .rRICTION FOR 4.ooo I~CH DIA/iETJi.R BLADE
....... o.4 Ol
i I
-5 ~ o.2~--------..i.--------...1----------..1..--------....a. .... --------.._--------..a.--...... •.-1
0
o.6
0
o.4
D
0
D
Curve-fit for computer
BEARING FRICTIOU FOR 4.039 INCH DIAl·lETER BLADE
O These measurements taken immediately after blade installed and before any fluid introduced into the exchanger.
NOTEa The 0-ring seat in the bearing which malfunctioned before t~e J.Soo inch diameter blade was removed was deepened in order to lessen .bearing friction with the 4.039 inch diameter blade.
O These measurements taken after the exchanger ··was operated for more than one hour.
0·\L-"'----...;....~-------2~0~0------__,, ______ '-'!"'40•0----..... --""-------~6~00---'
Agitator Speed (revolutions/minute)
Figure 7. Bearing Friction for the 4.000 and 4.039 inch diameter Blades
45
46
alignment while the blade diameter was being adjusted; an 0-ring might
have had to be replaced because it was damaged during exchanger opera
tion (this did happen while the 3.500 inch diameter blade was being
tested); the agitator might not have been placed in exactly the same
axial location in the exchanger for every blade; etc. From these
comments one mig~t well expect the bearing friction to change from
blade to blade and the bearing friction measurements show that it in
deed did change. The bearing friction is verr nearly linear with
agitator speed for low agitator speeds and approaches a constant value
for high agitator speeds. The curve-fits of bearing friction torque
vs. agitator speed used for computer data reduction are shown as solid.
lines on the above mentioned figures. For low blade speeds the data
were fitted with a linear relationship; above a certain blade speed
the data were fitted with a constant bearing friction torque. This is
a:s sophisticated a curve-fit as the data merit. The linear relation
ship fits the data well at low blade speeds. The bearing friction was
a much larger portion of the total motor power output at low blade
speeds than at high blade speeds; it was as much as 25 percent of the
total power requirements for the 3~500 inch diameter blade at the
lowest blade speeds and was·about 2 percent for the 4.038 inch diameter
blade at the highest blade speed tested. The only adjustment ma.de to
the agitator power measurements was that the friction torque was sub
tracted from the measured torque before the agitator power requirement
was calculated on the computer from the appropriate measurements. Both
the bearing friction torque and the agitator blade torque are listed in
the agitator power requirement data printout in Appendix D.
Later in this chapter it shall be shown that the bearing friction
47
does not have a significant effect on the final power correlation be-'
cause the slope of the power curve in the viscous regime is known to be
-1. This allows one to use the data points in the upper viscous regime,
where the bearing friction torque is a relatively small portion of the
total motor torque, to establish the position of the power curve for a
particular clearance.
Correlation of Power Data
Penney and Bell (36) have analyzed the theoretical work on screw
extruders and they have pointed out that theoretical solutions for the
creeping flow regime predict that for a flat blade of zero thickness
(the agitator power requirement of this system is defined as 11bulk
powern) the agitator power requirement can be represented by the follow-
ing functional relationship
= f ( ~j d~ .11J) (5-1)
We shall show now that this relationship holds outside the creep-
ing flow regime. In Chapter II it was pointed out that for a geometri-
( ~ i:fc . f>N3r::J 5 cally similar system the conventional power number
Nd'/ a function of the rotary Reynolds number ( ./1,< ).
) is only
For a system in
which the agitator is nearly as long as the containing vessel the power
should be almost directly proportional to the agitator length. This
requirement can be satisfied exactly by multiplying the conventional
power number by d, ~ 1 c. l!L \ ::. ~ 9c ... E . This power number, in-L /N 3d 5 U...) /Nb'~ - t:L.
volvingd 9L , retains geometrical similarity (it was multiplied by t ) and it satisfies the requirement that the agitator power requirement
must be directly proportional to the agitator length. We conclude that
;\, 5o /'N3J#J. will correlate the effect of length for systems in which
the agitator power is directly proportional to the agitator length.
Therefore the bulk power requirement for a solid flat blade of
zero thickness ca.n be represented by the functional relationship of
equation (5-1).
One would.expect that the power requirement of the knife-edged
flat blade of this investigation would exhibit essentially the same
power characteristics a.s a very thin: · flat blade would exhibit. If
this be the case, then correlation of the present agitator power re-
/i!'c quirement data on a. plot of,4v,t.,:,., vs. Re with C/D as a parameter
48
will suffice as a general method for prediction of bulk power·r.equire-
ments for a flat, solid blade. The data a.re so plotted in Figures 8,
9, 10, and 11 for the· .four blade diameters tested. Da.ta. with and with-
out heat tra.risfer fall essentially on the same curve. Figure 12 is a
composite of the correlations for individual clearances.
The slope of the curve of .. log' Pbi vs. log Re in the creeping flow
regime (Re<30) is known from theory to be -1. This fact allows one to
establish the position of the curve in the creeping flow regime while
neglecting the first four or five data points a.t the lowest Re where
the bearing friction is a greater portion of the total agitator power
requirement than at high Re. Thus the agitator power requirement •·
measurements a.t low torque have little effect on the final correlation
of ~L vs. Re.
Additional testing will have to be done to predict the clearance
power requirement and to determine if the bulk power requirement and
the clearance power requirement are for practical purposes independent
and additive.
PbL
100
10
1
LEGEND:
o Without heat transfer through wall 6 With heat transfer through wall
1 10 100 0.1 1,000 10,000.
Re
Figure 8. Agitator Power Correlation for the 3.500 inch Diameter Blade
+=""
'°
pbL
100 ~
lO
1
LEGEND:
o Without heat transfer through wall 6With heat transfer through wall
1 10 100 1,000 10,000 0.1-;-----------~-----------:::::----------~~----------....L----------__J
Re
Figure 9. Agitator Power Correlation for the 3.831 inch Diameter Blade Vl 0
1,000------~~~-,-----~~--~""T"~--~~--~-.~~--~----.--------------,
pbL
l.'00
10
LEGEND:
o ~ithout heat transfer through wall ~ With heat transfer through wall
1 ~---------~...._ ______________ .....
1 . 10 100 1;000 10,000
Re
Figure 10. Agitator Power Correlation for the 4.000 inch Diameter Blade \J'1 f-'
1,000
100
pbL
10
LEGEND:
o Without heat transfer through wall O With heat transfer through wall
1 -1 10 100 1,000 10,000
Re
Figure 11. Agitator Power Correlation for the 4.039 inch Diameter Blade v, l\)
100
10
J:bgc
'bL • r( d4t
1
1
d a 4.039; C/n = 0.00234
C/D .. 0.00715
c/n .. 0.0280
c/n • 0.0688
10 100 1,000 J.0,000
Re
Figure 12~ Correlation for Bulk Agitator Power Requirements of Flat Paddl.e Agitators V1 \;..)
54
The only other reasonably similar geometry for which data are
available are anchor agitators. The power results of Uhl and Voznick
(48) and Beckner and Smith (1) for anchors are compared with the pre
sent results :i,.n Figu:i;-e 13. PtL is plott~d vs. C/D at Re = 10. (The
straight-+ine correlations for different C/D are parallel in the creep-
ing flow regime; therefore, the value of Re chosen for comparison is
immaterial as long as it is in the creeping flow regime.) All the
data essentially fall on straight lines. Beckner and Smith I s (1) data
are compared using both the length of the agitator in the power number
and the effective peripheral len~th (EPL = L + D/4) in the power number
as suggested by Uhl and Voznick (48). The data correlate better if the
length of the agitator is used rather than the EPL.
If end effects are negligible, this agreement between the flat
blade and the anchor means that the blade arm width has little effect
on power over a wide range of blade arm widths. Uhl and Voznick (48)
found that a 2 inch and a 3 inch arm on a 24 inch diameter anchor'
agitator gave essentially the same power consumption. This indicates
that the power drawn by the anchors.is almost all bulk power. Penney
and Bell (36) esti.r:l]a.ted that the clearance power drawn by the anchor
agitators tested by Uhl and Voznick (48) was a maximum of 8 percent of
the total power consumption. One would expect that power consumed as a
result of end effects irl the present investigation would at least equal
or exceed the power consumed as a result of end effects of the anchor
agitators because the agitator of this investigation had two ends
whereas an anchor agitator has only one end which. consumes power. One
would not expect the free surface in the anchor tests to increase the
power requirement over that experienced at a solid surface.
Ptt
at
Re= 10
100
101-
l
~.
~.
I
~. ~~ ---------- o..._ ~~'-0
-.,, - ", -,'-a __ ............ , . .._ ~ -...... __ ~
LEGEND:
o This investigation
6 Uhl and Voznick Cis); 10 ?, inch vessel
• Beckner and Smith ( 1 ); Pt1oe 1/Le• where Le • L + D/4
o Beckner and Smith ( 1 ); PtLoc: 1/L
0 ........._. __ " 9'·-
NOTE: The data of Beckner and Smith ( 1) were extrapolated to Re • 10 at a slope of -1 on a plot of PtL vs. Re.
-
1~__,~--,--.~~~__,__,__,__,__,__,__,__,....___,__,__,~__,__,__,__,__,__,__,__,__,__,__,--,1.....___,__,~~~--.--,--,--,--,--,--,--,--,--,,-J
0.001 0.01 0.1
c n
Figure 13. Comparison of the Dependence of PtL on.£ for Various Data at Re • 10 D
1.0
\.rt \.rt
56
A comment is in order here concerning the inclusion of C/D raised
to a constant exponent in the power number. As Figure 13 indicates this
might suffice to correlate power in the creeping flow regime, although
one would not expect bulk power to satisfy any such relation as the
clearance approaches zero. The effect ·of clearance is very likely
different in the turbul,ent regime than in the laminar regime. If this
be the case, then C/D ca~ot be included in the power number if both
laminar and turbulent data are to be correlated on the same chart. In
fact, Uhl and Voznick 1s (48) data for the 24 inch diameter anchor in
dicate that the clearance has. little effect on power at Re~ 3,000.
Bates et al. (46) have pointed out that inclusion of geometrical ratios
in the power number is fundamentally unseund.
CHAPTER VI
EXPERIMENTAL AND CORRELATIONAL RESULTS
FOR HEAT TRANSFER
Eicperimental Results
Test were conducted with both ethylene glycol (the phy$ical pro
perties of the test fluids are given in Appendix C) and Gulf Harmony
Oil 151. Testing was done with ethylene glycol only for the 4.000
inch diameter blade.
The experimental variables which were monitored are given in
Chapter IV in the section entitled 11 0perating Procedure."
Wall temperature profiles and inlet and outlet temperqtures for
selected tests are presented in Figures 14, 15, 16, and 17 for each of
the four blade diameters tested. Data are presented for the creeping
flow (Re< JO) and transition ( 150 < Re < 700) regimes for each blade
diameter. Recall that in Chapter 5 we explained that as far as heat
transfer is concerned the flow is fully turbulent at Re= 700, although
it is not fully turbulent as far as agitator power requirements are
concerned until Re= .10,000.
In the turbulent regime the wall temperature is almost linear
except for & slight skewing down at the exchanger ends, indicating that
the heat transfer coefficient ;is almost constant along the length of
the exchanger. The skewness at the ends is probably a result of con
duction through the plexiglass endplate to the atmosphere or from the
57
150
130
1
temperatur.e
.... ~ _.-o- .. -0--
.... ~ ....a--....0- ~--. .--o-- ... ~ _--o--- .... _ A-- ... A- - --1::r- - -A- ... -
· Liqui~ temperature. __ . . _ _ _ ---0
------- ___ ,-4 ---- ------------- . ____ ... --~ A-~- --
temperature
Test Re
o 03/29/1810 ·7
i 100
•05/24/1430 9 .0.03/31/1914 256 o 03/31/2050 528
90
80
• t > ' > '
' ,, •
temperature
' • ' > « .. ;
,'_]=Liq~id o~----------~-~t!:_____ ______________________________________ o
70.__ ... _,.. _ _,__~ __ .._~~-.i...-...1:--....... -~--o 4 B 12 16 20
· Figure 14.
Distance from Exchanger Inlet (inches)., 21 ·
Typical Wall Temperature Profiles for the 3.500 inch · Diameter 13lade
58
17
C:r- -- ~,,,,,,,.
13
12
no
100
Figure .15.
---
_....o-_....c--. ...o-----a-.;_o--- . .
temperature
------- ... -i- --- - ------
Test. Re
o 05/17/170, 23 . A 04/27/1730 585 . 0 04/27 /1915 11917
Liquid temperature
Distance from Exchanger Inlet (inches)1• z
-- ... -A
Typical Wall. Temperature Profiles :£'or the 3 .. 8Jli ::hnch Diameter Blade . .
59
170
160
150
100
Wall te. mperatur~.. . . . . .. . . . . .· . · . - - ;.,A_,- -A,.... ..
.,... ..... ~ . . . ,,, . . _ ..a--_.a- - -o----::::a:--' ... ·--..A-- ---0-- .... __ ...0----.......,..,, ~
- y . . __ ..;..a
. ,,, /
a--- - ;:tf- - --.... --------- --------.---- -
., /
p
t::i,..----
Liquid temperature
--_... --- -----Test
---Re
o 09/15/1635 12 ~ 02/20/1520 309 0 02/20/1810 ~,077
--
Wall temperature
Liquid temperature
--- -:"
Distance from Exchanger Inlet (inches), z
Figure 16. Typical Wall Temperature Profiles :(or the 4.000 inch Diameter Blade · . · .
60
180
170
160
110
Wall temperature
Liquid temperature
,
Test
o 07 /07 /1640 A07/07/11{;.5 D 07/07/1120 • 07/05/1165
Re
2.3. ll 46
2.,233
.__:a___ . _ _n-- -a.__ -a...;.. -o---~ . . --:-0---
.,.,,...0-- Wall temperature
/~
8 12 16 20 Distance from Exchanger Inlet (inches).,. z
Figure l 7. Typi~al Wall Temperature ProfHes for the 4.039 inch Diameter Blade ·
61
62
endplate to the test liquid.
b. the laminar regime the wall temperature is skewed down at both
ends of the exchanger but more so near the entrance than near the exit.
Due to the development of an adverse temperature gradient as a result
of axial flow, the heat transfer coefficient would be expected to be
higher near the entrance than near the exit; probably it is this high
heat transfer coefficient near the entrance which causes the wall tem
perature to skew down near the entrance. The drop in wall temperature
near the exit is probably a result of conduction to the endplate and
very possibly the result of an increased heat transfer coefficient due
to end effects. It would be desirable to determine quantitatively how
the heat transfer coefficient varied near the outlet end; unfortunately
not enough 'Wall temperature measurements were taken to accurately
determine the axial variation of heat transfer coefficient near the
exchanger ends.
In the transition regime, the wall temperature profiles for the
3. 500 inch diameter and the 3. 831 inch diameter blade exhibit a minimum
near the center of the exchanger rather than near the ends. Thus in
this region the heat transfer coefficient is highest near the center of
the exchanger. This anomalous behavtor may be a result of secondary
flow in the exchanger.
The temperature profiles for the 4.039 inch diameter blade in the
transition and turbulent regime are not nearly so smooth as those for
the other blades. This behavior is probably a result of the clearance
not being constant along the length of the exchanger. The clearances
reported are average clearances. It is estinated the clearance for
the 4.039 inch diameter blade might vary as much as 0.005 inches. This
63
means that the clearance for the 4,039 inch diameter blade might have
varied from 0.005 to 0,0015 inches. This variation in clearance would
be expected to have little effect for the other blades.
Calculation of Experimental Heat Transfer Coefficients
The experimental heat transfer coefficient was calculated at 14
inches from the inlet end of the exchanger. At this location the
correction of axial conduction in the exchanger wall is most accurate
and the heat transfer coefficient is influenced the least by end effects.
where
The experimental heat transfer coefficient was computed as follows:
hl =1?- = (Tw - ~ ),g= If'-
qF = heat flux to the test fluid at z = 14 inches from the exchanger inlet.
= 2
-1- ....Lt- T ZZ L
..
(6-1)
(6-2)
(6-3)
A linear temperature rise is assumed between the fluid temperature
just inside the exchanger inlet (T0) which is T(14) on Figure 4 and the
fluid temperature just inside the exchanger outlet (T1) which is T(15)
on Figure 4, For the condition of axially constant heat flux to the
fluid the temperature rise of the test fluid would be essentially
linear. The heat flux to the fluid was not axi ally constant because of
axial conduction in the exchanger wall. I n order to minimize the error
in the calculated bulk fluid temperature due to nonuniform heat flu.x
64
axially, the temperature rise of the test fluid through the exchanger
was kept relatively small compared to (Tw - Tb)z ~ 14 except in the
turbulent regime where the wall heat flux was nearly constant axial:j.y.
Therefore, the error in the calculated bulk fluid temperature is net
expected to significantly affect the accuracy of the experimental heat
transfer coefficient.
Due to axial conduction in the aluminum wall, the heat flux to
the fluid (qp) at any axial location is not in general equal to the
constant heat flux from the heating element (qH). The heat flux to
the fluid can be calculated from the experimental wall temperature
profile. By assuming negligible radial wall temperature variations
and constant heat flux from the heating element, equation E-2 below is
obtained in Appendix Eby a heat balance on an element of wall.
If- (E-2)
The second derivative of wall temperature with respect to exchang-
er length was calculated by finite differences using the experimental
wall temperature measurements. In Appendix Ethe calculation procedure
· is explained and the finite difference calculations are compared with
graphical methods. The finite difference method was compared with the
hand graphical method for a series of 10 tests with the 3.500 inch
diameter blade. The maximum deviation of (qp/qH)z = 14 was 7.5 percent
and the average absolute deviation for the 10 tests was 2.4 percent.
The finite difference method appears to give less test to test random
error than the hand calculation method. The ratio qp/cm: was as low as
0.65 in the laminar regime and was essentially 1.0 in the turbulent
regime.
65
Correlation of Data
Uhl and Voznick (48) for anchor agitators show that in the turbu-
lent regime heat transfer is coTrelated very well by a plot of /v'v AiO,l '8' ;::;_ 1/3 't' vs. Re, if only agitator rotation affects the heat trans-
fer, This is the correlating mechanism which Uhl and Voznick (48) use
in the laminar and lower turbulent regimes. ln the laminar regime the NP ¢0.1~
straight-line correlations of ~~~ vs. Re on log-log graph
paper has a positive slope of! which :makes the exponent on Re equal!.
Their correlation then predicts that the heat transfer coefficient is
proportional to the fluid viscosity of the -1/6 power. In the creeping
flow regime for isother:rnal radial conditions, however, the fluid flow
patterns are independent of the fluid viscosity; therefore, the heat
transfer coefficient should be independent of the fluid viscosity. In
order for a plot of /VtJ ¢0./8' /Jrl/3
vs. Re to correlate heat trans-
fer in the creeping flow regime the slope of the resulting straight-
line correlation must be 1/3 so that the viscosity in both Pr and Re
'Will cancel.
The heat transfer results of this investigation are correlated by
this method in Figures 18, 19, 20 and 21. Data were taken for ethylene
glycol only with the 4.000 inch diameter blade and only in the turbulent
regime. The data for oil and ethylene glycol agree very well. In the
turbulent regime the data for all clearances very nearly coincide. In
Figure 22 the correlation of the present investigation is compared with
the correlation of Uhl and Voznick (48) for anchor agitators. Again
the correlations very nearly coincide in the turbulent regime. As a
further check of the generality of this correlation in the turbulent
regime, Uhl (46) has compared Votator data in the turbulent regime with
1oor---....... ~----r-~--------,--------~~-,------------,,------~----
10
ID!- ~w)o .18
Prl/3 b
l
a. @ 0
8 0
6 IIJJ )6 .&
~ • •
0
8 0
A eao
. Q,; oo o m lo i,e• ·
o'9aeo~lee• . -
LEGEND:
Tests
a 05/24/1355-2000 e 03/31/1110-1415 o 03/29/1620-2130 A 03/31/1643-2050 & 04/03/1500-1840
Re a
0.2-0.4 0.4~0.5 0.7-.1.0 2.6-3.0 B.0-9.0
(Tw-Tb)
16-65 24-42
1.7-40 6-65
13-21
0.11~------~~t;-~~~~~~-----~--~~::::--~--~--......J..~--_..--._.._J 10 100 1,000 10,000
Re
Figure 18. Heat T.ransfer Correlation .for the 3. 500 inch Diameter Blade
°' °'
100
!ig__ lfw)o .18
Prl/3lP b
101-
11-
-1 I
ee&eo.~ol~
~8
A • ~
A
l
flj AC. ~
t:P,A
46
4/:i' AIJAe
•• 9 LEGEND:
Tests
& 05/17/1140-2330 o 04/23/1455-1832 e 04/26/1135-1937 ~ 04/27/1550-1915
I
Re (T -Tb) a w Oo4-0.9 2.7-70 0.8-LO 50-67 0.7-1.8 4.6-80 2.6-4.2 4-70
-
a
o.1~~~~~~_,;,~~i..-~~~--~~ ....... -..i---~~~~~~~.....i.~~~~~~~~--~~~~~~~~---1 10 100 1,000 10,000
Re
Figure 19. Heat Transfer Correlation for the 3$831 inch Diameter Blade
0---.J
Nu {~w) Prl/3\f1b
1,000 • LEGEND:
Tests
o 09/15/1120-2105 & 02/20/1300-1810 e 10/08/1230-1735 A 10/09/1355-1720
100 t- 0 07/09/1250 to 07/14/1415
in 1965 0.18
10 1-
Re a
1.5-204 3.1-4.3 5.0-6.0 6.0-9.0
200-260
• I
(Tw-Tb} Test Liquid
11-27 4-18
12-30 5-11
3-45
GULF HARMONY OIL 151
ETHYLENE GLYCOL ,.~
~& .. ,Jt .... ~ . •. p .
e
a a• o ti
eo oe~oo0 '9
o o ocPo o o ~ a 3'
-,
0 §Q:o
8 08.
-
-
la-e--~~~~~~5-1~~~----~~-------..------....,.----.....i.~--~"""'"--..-..... ...,..-i.~~~ ...... ~~~~..J 1 10 100 1,000 10,000
Re
Figure 20. Heat Transfer Correlation for the 4.000 inch Diameter Blade
a-co.
1,000 J - ·
100 I-
0.18
l Nu rw) Prl/3 _jAb
10 I-
1 1
LEGEND:
Tests Re a (Tw-Tb)
e 07/27/1220-1730 0.9-1.0 21-55 & 07/07/1050-1715 1.0-1.2 21-52 o 06/27/1220-1730 1.7-3.2 7-47 t:J. 07/05/1100-1455 5.3-8.0 14-33
o.A ~-
(> e:.O . o°'
4>°' 0
0
8 o e £ e .._.e o O ,.,. 0 Cl)
6
•• 6 6 et 6
10 100 1,000 10,000
Re
Figure 21. Heat Transfer Correlation for the 4.039 inch Diameter Blade
-
.
°' '°
1.,000,,----------"l-"'----------------------------,.----------.
100
~ . {fw)0.18 Prl/3 \f\
10
1
~~~~This investigation
- - - Recommended correlation of Uhl and Voznick (48) for anchor agitators., C/D = 0.009 - 0.07
C/D = 0.00234
C/D = 0.00715
C/D = 0.0280
C/D = 0.0688
10 100 1.,000 lOllOOO
Re
Figure 22. Heat Transfer Correlation
--..J 0
the suggested correlation of Uhl and Voznick (48) and has found good
agreement. This indicates that neither clearance nor geometry has a
significant effect on heat transfer in the turbulent regime.
71
Now consider the laminar regime where free convection and axial
flow are likely to affect the heat transfer. In the creeping flow and
transition regimes (as noted in Chapter II the creeping flow regime
extends up to approximately Re= 30) the data of this investigation
are obviously affected by axial flow and probably by free convection
also. The data for the 3.500 inch diameter blade in Figure 18 show
a pronounced effect of axial flow below Re= JO. The data for the
J.831 inch diameter blade also show a slight dependence on axial flow
for Re below 100. The data for the 4.000 inch diameter blade are
scattered in the laminar regime due to greater errors for this blade in
computation of the second derivative to obtain the wall conduction
correction. For the 4.039 inch diameter blade it appears that free
convection affects the heat transfer at the lowest blade speeds (as
low as 5 rev./min.). The increase in heat ~ransfer below Re= 10 is
probably due to the blade speed being so low that the buoyancy forces
have sufficient time during a single revolution of the blade to estab
lish free convection flows before the gravity vector changes direction
1"1"ith respect to the blade velocity vector. The effect of axial flow
is probably negligible for the 4.000 and the 4,039 inch diameter blades
because the heat transfer due to the blade rotation is so much higher
than for the 3. 500 inch diameter and the 3. 831 inch diameter blades.
There was also some anomalous behavior of the outlet temperatures
observed for the 4.039 inch blade which may have some bearing on the
minimum in the heat transfer in the laminar regime. Figure 23 presents
-~-~---t-~---+-~~+-~-t--+-~~1---~-11~~----1-~ _... - "'I -- - I -u'-'.1. 1.. o ... --..... ....., ..... .,_ ._ ...,..,.. .... ed: L · I"')("\ ..: -- -·L...-.,....,, ........ -: 'V'\ 1,-'- - , (\ .;,--k-..-. /.,_.: -· i.:.e:.-
~---h-~~1------~--~-t-~--+-+-~---+------~-~~--
I I
l J
Time of Test: 07/07/1715 Agitator Speed: 249.2 revolutions/min. Re: 133. 5 Temperature Scale on Chart: 0.5 mv/in.
I I ----,· - - ,., - -... 1- ""' T I I I I II l I I I I - -, '
I ..
I ..-- ~
I II ;J f> II
" -'.V-- I r r.
' II -·-i ' ; +-1
I 1-- I I ----· 't-}_f::--'--i -
l I .., l J t l ... Ut--:-~--- f-- \ J
-·r r1rc. .::, ·--· . .., 1;n~n""'_~1 I'm, n, __ :c-e--~+-----= .
Time of Test: 07/07/1605 Agitator Speed: 5.2 revolutions/min. Re: 2.6 Temperature Scale on Chart: 0.5 mv/in.
Time of Test: 07/04/1715 Agitator Speed: 40.7 revolutions/min. Re: 21.3 Temperature Scale on Chart: 0.5 mv/in.
Figure 23. Strip Chart Recorder Traces of the Millivolt Output of Thermocouple 12 in the Exchanger Outlet Line for Selected Tests with the 4.039 inch Diameter Blade
72
73
strip charts from a Brush Recorder of the temperature in the outlet line
for the tests below Re= 300. At Re= i30 all temperatures were steady
with little fluctuation. At about Re= 100 the outlet temperature
started fluctuating± 3°F in a .random manner; at about Re.= 20 the
random fluctuations were about± 5°F, for which the total fluctuation
is approximately equal to the temperature rise through the exchanger.
The period of the fluctuations varied from about! to 1 minute. At Re
below 10 the random fluctuations in outlet temperature did not exist
although periodic fluctuations caused by the rotating blade did exist. ! f
We do not know how this instability might affect the heat transfer. The
instability was not noted for blades other than the 4.039 inch diameter
blade. It was very noticeable pn the potentiometer. The potentiometer
galvanometer would go all way off scale on both ends during the greate'st ;
fluctuations. For. other blades at the s9'me Re the galvanometer was
steady.
Because free convec,tion and axial flow affect the heat tr9-nsfer at
low blade speeds, the slope of the curve of ~;'v3 cf · If? vs. Re
cannot be established with certainty in the upper creeping flow regime.
If this correlating m~thod is correct, however, then in the creeping
flow regime the slope must be 1/3. With the data available. in the
creeping flow regime, there is certainly no justification for using
any other correlating method than the one used. In order to compare
the heat transfer for the various clearances, the slope is assumed 1/3 i I
and Figure 22 presents a composite of all the data.
There are some very important points to be made· from this1,,:figure'. ·;fl!'
•, ;,'',.·' .. ·r' I
The clearance has a great effect on the heat transfer in t/h$.-,:laminar
regime but not in the turbulent regime. ln the transitioi-i,:.'regime the
74
the heat transfer increases greatly over a very narrow range of Re.
For the 3.500 inch diameter blade a ten-fold increase in heat transfer
is obtained as Re doubles from 150 to 300. Clearance and agitator
geometry have little effect on heat transfer in the turbulent regime.
If Uhl and Voznick•s {48) data in the laminar regime are not infiuenoed
by free convection or other extraneous effects, the agitator geometry
does have a great effect on heat transfer in the laminar regime, espe
cially for large clearances. The largest clearance used in this in
vestigation gave heat transfer rates 1/7 those of the largest clear
ance used by Uhl and Voznick (48) at Re= 100. The largest clearances
of this investigation had approximately the same C/D as the largest
clearances used by Uhl and Voznick.
Discussion of the Possible Effects of Axial Flow
and Free Convection on the Experimental
Heat Transfer Coefficient
After calculating the experimental heat transfer coefficient the
next consideration is whether this coefficient is influenced by
extraneous effects, i.e., effects on other than agitator rotation.
The primary factors which can affect the heat transfer (assuming
constant fluid physical properties) are (a) free convection and (b)
axial flow. Both these factors should affect the heat transfer more
at low blade speeds than at high blade speeds.
The driving force for free convection is gravity, which always
acts in a vertical plane. Because the rotating blade, and thus most of
the test fluid, continually changes position with respect
to the gravity vector, the free convection tends to be canceled by blade
75
rotation and also at high blade speed the rotational convective forces
tend to overshadow the free convection forces. Also free convection
generally diminishes as the blade speed increases because the bulk
fluid to exchanger wall temperature in general decreases as the blade
speed increases. Thus free convection would only be expected to affect
the heat transfer at very low blade speeds (i.e.) low Re),
The axial flow produces fluid flow which is essentially perpendi
cular to that produced by blade rotation. The effect of axial flow
can be determined experimentally by conducting tests at various axial
flow rates. We attempted here to conduct tests at sufficiently low
axial flow rates so that the heat transfer coefficient was affected
only by blade rotation. The final heat transfer correlation in Figures
H\ 19 3 20 and 21 indicate that we were successful in attaining this
objective except at very low Re.
CHAPTER VII
EXPERIMENTAL ANP CORRELATIONAL RESULTS FOR THE EFFECT
OF BACKMIXING ON THE MTD
Analysis of Experimental Data
The only experimental measurement made in this investigation which
can be used to determine the true MTD and thus the effect of backm:ixing
on the MTD is the temperature just inside the inlet line of the ex-
changer (T0). The dimensionless parameter involving the temperature
just inside the inlet line, which can be related to analytical solutions
of the dispersion model 3 is the temperature jump ratio ~ -7;· = -(f!J,.-~- ~ where Ti is the temperature at the exchanger inlet and T1 is the tem-
perature at the exchanger outlet.
Figure 24 presents temperature jump ratio data from selected
tests plotted vs. Re. These data were selected in order to show
differences between datafromdifferent blade diameters operating at
-~essentially the same conditions and to show the effect of axial flow
rate for a particular agitator. Note the great difference between the
data for the 3.500 inch diameter agitator and the data for the 4.039
inch diameter agitator taken 06/27/1220 although both sets of data are
for essen~ially the same operating conditions. Also note that the two
series of tests for the 4,039 inch diameter agitator show that the
temperature jump ratio is higher (i.e. the MTD is lower) for lower
axial flow rates.
76
T0 - T. . J.
TL - Ti
1.0 I
o.a t-
o.6
o.4
0.2
d
• 3.500 A 3.831 o 4.000 ~ 4.039 0 4.039
Tests
04/21/1053-1620 05/17/1140-2330 02/20/1300-1810· 06/27/1220-1730 07/~5/U00-1455
Rea w
o.69-1.23 0.4-0.9 3.4-4.3 1.7-3;2 5~3-B.o ·
, 216-224 103-ll5 174-177 185-200 378-412~-t>~- o
/. 0 ........... A~~ "O,
' -~<;--.-O e"'"
. A .. ,, ,• .
" I ... ~ ,_"', , . ,,,. , r ,, ....... \ 'j ..,......... \ •• / • ._ I • ,-e'// ....... ,
,
/' 0 / ID /
100 1.,000
Re
Figure 24. Selected Temperature Jump Ratio Data
10.,000
--.J --.J
78
The accuracy of the temperature jump ratio and thus the accuracy
of the calculated dispersion parameter wa.s primarily dependent upon
the accuracy of the exchanger outlet temperature TL. In the laminar
regime substantial radial temperature gradients existed in the excha.ng
/ er outlet line; the three thermoc~uples in this line, the locations of
which a.re given in the "Temperature Measurement" section of Chapter IV,
in some cases deviated from one another by as much as 5 F. Consequently
TL wa.s calculated from a heat balance in the lam:µiar regime. The
measurements in the turbulent regime where tpe outlet line is essen-
tially isothermal indicate that the heat balance closes only within 10
to 15 percent. Then the denominator ofi "1>; , namely (T1-Ti), may be in
error by as much as 15 percent in the laminar regime; therefore, assum-
ing that r0 and Ti are not in error, -ET may be 15 percent in error.
There is also some question, which unfortunately cannot be resolved
with the present experimental apparatus, as to whether the temperature
indicated by the thermocouple just inside the exchanger inlet was the
true local bulk fluid temperature. The hottest and coldest regions of
the liquid in the exchanger periodically moved past this .thermocouple,
but it still might not have indicated the true local bulk temperature.
This temperature would be expected to be more in error in the laminar
regime than in the turbulent regime. There is one indication that it
did indicate a true local bulk temperature: when the effect of back-
mixing wa.s negligible, T0 wa.s very nearly equal to Ti.
Application of the Dispersion Model to the Present 1.' ~
Ex:perimental System
The effect of backm.ixing on the MTD is here interpreted in terms
79
of the dispersion model. As has already been pointed out in Chapter II
the dispersion model of the backmixing phenomena is a one-·parameter
model ( that parameter is cx.E). The effective thermal diffusivity
(~) has to be determined from experimental data by use of theoretical
solutions of the dispersion model.
Certain assumpU,ons have to be made in order to obtain analytical
solutions of the dispersion modeL The major assumptions for the
analytical work done here are as follows:
(a) constant effective thermal diffusivity
(b) constant heat transfer coefficient
(c) no axial d;ispersion in the inlet and outlet lines
With these basic assumptions analytical solutions which are perti
nent to obtaining meaningful values of cxE from the experimental data
have been obtained in Appendix A for the following special cases~
1. constant wall temperature
2. constant wall heat flux
3, constant wall heat flux with infinite axtal conduction in the
t·fgitator (Le, the thermal conductivity of the agitator is
assumed infinite).
The closed analytical solutions to the above three special cases
are given in Appendix A as equations (A-14, A-27 and A-47), respective
ly. These equations shall not be given in this chapter because graph
ical representations of the relationships expressed by these equations
are much more instnictive than the equations. The functional form of
the analytical results for each special case is as follows:
For constant wall temperature.
GJ-= j (?e.1;6) (7-1)
For constant wall heat flux:
fl) = j(?e) (7-2)
For constant wall heat flux with infinite a.x;ial conduction in
the agitator:
e=fC~,8') <1-3)
Here t8:. h ,4 is . the number of transfer units for heat transfer from We VL
the exchanger wall, Pe=~ is the axial dispersion Peclet number
and ,tf '= h/M ,44 is the nU:er of transfer units for heat transfer to c 7;-7;'·
and from the agitator.-(!!)~ is called the temperature jump Z:-- Z""· c...
ratio.
Figure 25 presents the relationships of equations (7-1), (7-2)
and (7-3) in graphical form. The solution for the constant wall tern-
perature case is exactly the same as for the case of constant wall
heat flux with infinite axial conduction in the agitator with ;!? I replaced by~ • The case of constant heat flux can be considered as
being a limiting case of the two other cases;
solutions for the other two cases when jS = 0
it is the same as the /
or ;5 = 0.
The conditions of this investigation, especially in the laminar
regime, are neither constant wall temperature nor constant heat flux.
Note, however, from Figure 25 that the dependence of Pe on -(5}-- is the
same for the constant wall temperature case and the case for constant
heat flux with infinite agitator canduct;i.on if ~ and ;1J I are
sufficiently small. If it is assumed that h = ri,, then it is shown in
Appendix A thatf -0.64. Thus if tests are conducted at small
values of~, the solution for the constant heat flux case can be used
to determine meaningful values of °'E from experimental temperature
q> (TO-Ti) TL-Ti
' . I 1.0,~-===::::::~--,-, ---.----o.a
o.6
o.4
0.2
~ = '!}! We
p' .. hAAA We
constant flux
Iw-----
Ti
I /), pa 20
t i~~ ol I 0.05_/ ~
0.01
Figure 25.
0.1 1 10 Pe .,, UL
~
Temperature Jump Ratios from the Dispersion Model for the Cases of (l) Constant WaU Temperature and (2) Constant Wall Heat Flux with Infinite Conduction in the Agitat©l'f
100
00. r>
jump ratios provided that the assumptions (a), (b) and (c) above are
reasonably satisfied.
82
Unfortunately these assumptions deviate considerably from physical
reality in the laminar regime. With respect to assumption (a) of a
constant axial dispersion coefficient, the dispersion model has been
shown to represent the backmixing phenomena in turbulent flow, partic
ularly for flow through pipes; it has not been shown to represent the
backm:bcing process for laminar flow in agitated systems where the back
mix:i.J;lg possibly arises from secondary flows which is possibly the back
mi.x:ing mechanism for the thin, flat-blade agitator.
Assumption (b) of constant heat transfer coefficient is a very
good approximation in the turbulent regime. In the laminar regime it
was pojnted out in Chapter VI the heat transfer coefficient was gener
ally higher near the center of the exchanger than near the ends of the
exchanger and, in particular, it was pointed out that the developing
adverse temperature gradient at the inlet results in higher heat trans
fer coefficients at the inlet than at other axial locations. This high
heat transfer coefficient just inside the exchanger inlet causes the
temperature irrnnediately inside the exchanger in.let to be higher than it
would if the heat transfer coefficient were constant axially. In turn,
when Pe is computed from measured values of -B- it is less than the true
value of Pe; this results in computed values of C><'.E that are higher
than the true values. Thus one would expect that the calculated values
of °"'2:: might be larger than the correct values of c;>c'.E in the laminar
regime.
Correlation of C1iif in Ter~ of the Operating Parameters
of the System
83
o.'.e was calculated from the. experimental temperature jump ratio
data from the analytical solution for the case of constant heat fluxo
The curve of o<.e vs. Pe in Figure 25 for the case of constant heat flux
was curve-fitted in three portions to get Pe explicitly in terms of
The curve fits are documented in the computer pragram. whioh is given in
Appendix D.
The dispersion parameter~ wa.s correlated with the operating
parameters of the agitated heat exchanger by the method used. by
Croookewit, Honi1 and Kramers (14), which is &nalcgous to earlier corre
lations for axial flow in pipes. ~/vtDe was plotted vs. Re.
Correlations for the different blades are presented in Figures 26, 27,
· 28 and 29. Except for the 3 .500 inch diameter blade the correlation
brings the data for different axial flow rates together. The results
of this correlating method for the various blades are compared in an
approximate manner in Figure 30. 'r:tie data for the 3 .500 inch diameter
blade and the 3.8.31 inch diameter blade are sufficiently close together
so that they are represented by a. single curve in Figure .30 and like
wise for the 4.000 inch diameter blade and the 4.039 inch diameter
blade. In the laminar regime the effective thermal diffusivity for the
two largest clearances is DDlCh larger than for the two sma.llest clear
ances. This may be a result of the "simple-one parameter dispersion
model." not representing the dispersion phenomena in the laminar regime,
or it may be because the heat transfer coefficient was so DDlCh higher
near the inlet than near the outlet for the large clearances or a com
bination of the two.
0.1 I
0.01-
A
o(, E
vtDe
0.001-
I
e
I • • ... e .... •,., 6 6
e
I
LEGEND:
Tests
A 05/24/1147-2225 6 05/30/1506-2150 e 04/21/1053-1620 e 06/01/1625-2045 o 04/03/1500-1840
4 A Aoo·A
Ao
•e 6 O O
A f Cb o c»o 0//>o
A A. . 11 .. • A e . 6-
666~ A
w
.72-86 185-193 216-224 185-209 595-610
l
Rea ,B 0.2~0.6 0.24-2.2 0.3-1.7 0.24-1.9 0.7-1.2 0.15-2.0 1.0-1.7 .. -0.15-2.6
. 8.0-9.0 0.41-0.72 -
-
o.0001 ................. -...--------_,_ ____________ .._ __________________ ...._ __ ....., __________ ...,., ______________ __.
1 10 100 1,000 J.O,ooo
Re
Figure 26. Axial Dispersion Correlation £or the 3.500 inch Diameter Slade ffe
0.1
0.0111-
£XE ·vtDe
0.0011-
0 .. 0001 l
I I I I
•
•aa
o9 0
~ - eo CD e• e o flt e
& e q, 0 e • &46 e ~ ~
- 0 °"""'... • ! --~'\, 6 6 A El, AA 6 &A J.c:t
-e
LEGEND:
Tests w Rea fi' -. 6 05/17/1140-2330 103-115 0 .. 4-0.9 0.25-7 .. 3
O 04/23/1455-1832 238-242 0.8-1.0 0.15-0.23 e 04/26/1,135-1937 244-260 0.7-1.8 0 .. 13-2.2 It 05/14/1455-1915 235-244 1 .. 7-2.8 0.23-2.0 A 04/27/1550-1915 223-233 2 .. 6-4 .. 2 0 .. 23-4.2
I I l I 10 100 1;000 10,000
Re
Figure 27., Axial Dispersion Correlation for the .3 .. 831 inch Diameter Blade &;
0.11
0 •. 011-
o(E '\De
0.0011-
LEGEND:
Tests
e 02/18/2035~2305 O 02/18/1620-1955 A 02/20/1300-1810
w
314-316 385-388 174-177
Rea
2.0-2.8 2.1-3.2 3.1-4.3
t9 0.29-0.93 0.25-0. 72 oo 0.62-3.80 0
·~
o,;r,, 0 'i , fL
e eeo
e 0 o
0
0 0
000 -00
-
0.0001,._ ......... __ ....... __ ...... __ ~--------------~--------------""'!""~~---------"""""""""'!!~!"'!"!' ....... ____ .......,,__ __ __. 1 10 100 11 000 lO~OOO
Re
Figure 28.. Axial Dispersion Correlation for the 4.000 inch Diameter Blade ro °'
0.1 I I I I
O.O]f- -A
A Ao o °o A
o<. I AG
_L O t9
't. De • 0
LEGEND:
o.ooJJ- Tests w Rea ;;, -o 06/27/1220-1730 185-200 1.7-3.2 o.46-3.3 A 07/05/1100-1455 378-412 503-8.o 0.62-1 .. 5
0.00011 ______________________________ ~-----=""""""""""""""""""""'...,,,.,s 1 10 100 1,000 10,000
Re
Figure29o Axial Dispersion Correlation for the 4Q039 inch Diameter Blade ~
o.
o.o ~
.vtDe
or
A. Vt De
0.001
Dm '7(D = o.611D De = 2 + 7f
Agitator geometry for this investigation
~e•D-d
-
I
Agitator geometry for the investigation of Croockewi Honig and Kramers (14)
,:----_ ......__
----- .............
I LEGEND:
----This investigation for d = 3.500 and 3.831 inches. ---This investigation for d = 4.ooo and 4.039 inches ..
, ----Mass dispersion data of ·Croockewit, Honig and
tbrough a.11 annulus with the inner cylinder rotating. I Kramers (14); NH4Cl dispersing in water flowing
0.0001 ~ l 10 100 n 1 21 000 101 000
Vt '"'e
Ree .. ;P
E'igure 30.. .Axia.1. Dispersion C;;irrela,tion ():). cx;i.
o.6 £
(i'IT'D ) UIT'D
0,.4
0.2 p .. ~
O I
0.01 0.1 l
l .. ~ Te 'uL
0.1
10
Figure 31. · Tbe Effect of Axial Dispersion of' Heat on the i'ITD from the Dispersion I'lodel ·
M
0.5
l
2
10
20
100
co. '°
90
The data compare reasonably well in the turbulent regime and they
also compare reasonably well with data for axial dispersion of mass in
an annulus with the inner cylinder rotating. The correlation of
Figure 30 uses an equivalent flow channel diameter (D) in both the e
dimensionless dispersion parameter and also in the Reynolds number.
This correlation indicates that the dispersion model will probably
adequately represent the dispersion phenomena. for design of mechanical-
ly-agitated equipment in the turbulent regime. It also indicates that
the dispersion model may not be adequate to represent the dispersion
phenomena in the laminar regime,
Design Method for Predicting the Effect of
Bae kmixing on the MTD
',l.'he presentation of the results of the dispersion model in Figure
25 is necessary in order to obtain O(_ E from values of e obtained from
measurements but this chart cannot be used for design purposes. For
design purposes one fixes exterior temperatures and not T. The 0
dispersion model for the constant wall temperature case can be recast
in terms of the ratio of the true mean temperature difference (MTD) to
the logarithmic mean temperature difference (LMTD). The mathematics of
this operation are given in Appendix A. In Figure JO the ratio of MTD
to IMTD ( ) is plotted vs. 1/Pe with as a parameter. This plot can
be used for design purposes if correlations are available for heat
transfer coefficients and the effective thermal diffusivity.
The assumption of constant wall temperature will probably repre-
91
sent physical reality well in most design cases because the temperature
change of the process stream is generally much greater than the temper
ature change of the cooling or heating medium.
Once the MTD has been determined the area of the heat exchanger
can be determined from the familiar expression:
~(h) (Mr.o)J The heat transfer coefficient for agitated heated exchangers with
flat blade agitators could probably be determined with sufficient
accuracy for most design purposes with the results of this investigation
if 1/D for the exchanger in question were longer than 1/D of the test
exchanger used here.
The design information discussed here is strictly applicable only
if the exchanger wall temperature is constant and if the heat transfer
coefficient is constant; however, it will find practical application in
many cases when these conditions are pot strictly met simply because it
will be the only or the best design information available.
CHAPTER VIII
CONCLUSIONS, COMMENTS AND RECOMMENDATIONS
Agitator Power Requirements
(1) The agitator power requirements for the knife-edged flat blade
tested here have been correlated by.plotting ,pbL vs. Re with
C/D as a parameter. This correlation appears to be completely
general for this agitator; it can probably be used to predict
agitator bulk power requirements for flat blades with non-zero
thickness near the vessel wall.
(2) The power consumption for the knife-edged flat blade agrees with
power consumption for anchor agitators within 30 percent when
compared on a plot of PtL vs. Re with C/D as a parameter. This
agreement indicates that anchor arm width has little effect on
agitator power requirements over a wide range of arm widths, if
the free surface in the case of the anchor tests does not affect
the agitator power consumption significantly.
(3) Additional work is needed to determine the effect of the blade
thickness on agitator power requirements.
Heat Transfer Coefficients
(1) In the turbulent regime neither agitator geometry nor clearance
has a significant effect on heat transfer over the range tested.
(2) For large clearances in the transition regime a small change in Re
92
93
effects a very large change in heat transfer. For small
clearances the change is much smaller.
(3) For large clearances the heat transfer for anchor agitators in the
laminar regime is up to seven times higher than for the flat blade
at the same Re and the same c/D. This indicates that agitator
geometry may have a considerable effect on heat transfer in the
laminar regime.
(4) In the laminar regime small clearances give much higher (up to
seven times higher for this investigation) heat transfer than do
large clearanceso
(5) Additional work is needed in the laminar regime to determine the
proper correlating method in this regime. In particular tests
should be conducted with a viscous fluid which has thermal
properties widely different from the oils previovsly used. The
effect of agitator geometry should also be studied in the creeping
flow regime.
The Effect of Backmixing on the MTD
(1) The solutions of the dispersion model for the cases of constant
wall temperature and constant heat flux have been put into con-
venient form for calculating dispersion parameters from experi-
mental temperature measurements.
(2) For the case of constant wall temperature the solution of the
dispersion model has been put in convenient form for use in heat
exchanger design.
(3) The dispersion data of this investigation were correlated using a <::>,,tE
previously suggested correlation of plotting UD. vs. Re. This 6 e
method correlated both the effect of axial flow and clearance in
the highly turbulent regime, and it adequately correlated the
effect of axial flow; but it failed to correlate the effect of
clearance in the laminar regime.
94
(4) The dispersion model probably adequately represents the dispersion
phenomena in the turbulent regime but it may not adequately re~
present the dispersion phenomena in the laminar regime.
(5) Additional work is urgently needed to develop methods to describe
the axial dispersion phenomena in the laminar regime.
Recommendations for Obtaining More Accurate
and Meaningful Data
There are certain improvements to the experimental apparatus which
would give more accurate data, The accuracy of the heat transfer
coefficients in the laminar regime could be improved by doing any or
all of the following: make the exchanger longer, decrease the exchang
er wall thickness and/or construct the exchanger of a material with a
lower thermal conductivity than aluminum. The heat balance could be
improved by either or both of the following: thoroughly I)ri.x the outlet
fluid before measuring its temperature and/or measure the flow rate
through the exchanger by a weighing technique.
Temperature measurements at other radial locations just inside
the exchanger inlet would be helpful to determine if the temperature as
obtained here is truly the fluid bulk temperature at that location.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
. (9)
(10)
(11)
(12)
A SELECTED BIBLIOGRAPHY
Beckner, J. L. and Smith, J. M., "Anchor-Agitated Systems: Power Input with . Newtonian and Pseudo-p4stic Fluids, 11 Trans o
Instn.Chem. Engrs~, W±. (6), T244 (1966).
Bell, K. J., Personal communication (1964).
Bernhardt, E. c., (Editor), Processing 2£ Thermoplastic Materials, SPE Plastics Engineering Series, Chapter 3 (1959).
Bischoff, K. B. and McCracken, E. A., "Tracer Test in Flow Systems,". Ind. and Eng. Chem., 58 (7), 3 (1966).
Bischoff, K. B., "Mixing and Contacting in Chemical Reactors," Ind. and Eng. Chem., ~ (11), 18 (1966).
Bolanowski., J.P. and Lineberry, D. D., "Special Problems of the Food Industry, " Ind, and Eng. Chem. , ~ (3), 657 ( 1952) •
Boey, M. L., "Infleunce of Channel Curvature on Flow, Pressure Distribution, and Power Requir.ements of Screw Pumps and Melt Ex:truders," SPE Trans., 3., '17-6,, (Ju1f 1963).
Bourne, J. R., and Butler, H., "Some Characteristics of Helical Impellers in Viscous Liquids," Paper No. 9 in Vol. 10, Mixing=Theory Related to Practice, A.I.Ch.E. and Instn. Chem. Engrs. Joint.Meeting, London (1965) •
Brown, R. W., Scott, M.A. and Toyne, C., "An Investigation of Heat Transfer in Agitated Jacketed Cast Iron Vessels," Trans. Instn. of Chem. Engrs., 25, 181 (1947).
Calderbank, P. H., Moo-Young, M. B., " .. The Powe; Characteristics of Agitators for the Mixing of Newtonian and Non-Newtonian Fluids, 11 Trans. Instn. Chem. Engrs., ll, 22 (1961). See the cover sheet of Vol.~ (1962) for important correction to equation 12.
Chapman, F. S., and Holland, F. A., "A Study of Turbine and . Helical - Screw Agitators in L:iqu_id Mixing, 11 Trans. Instn. Chem. Engrs., !:l:J., T131 (1965).
Chapman, F. A. and Holland, F. A., Liquid Mixing and Processing in Stirred Tanks, ~einhold Pub. Ca., New York (1966).
95
(13) Chilton, T. H., Drew, T. B. and Jebens, R. H., 11Heat Transfer Cqefficients in Agitated Vessels," Ind. and Eng. Chem., .2.£ (6), 510 (1944L
(14) Croockewit, P., Honigj C. C. and Kramers, H., "Longitudinal Diffusion in Liquid Flow Through an Annulus Between a Stationary Outer Cylinder and a Rotating Inner Cylinder," Chem. Eng. Sci. ~, (1), 111 (1955).
-(15) Dankwerts, P. V., "Continuous Flow Systems - Distribution of
Residence Times, 11 Chem. Eng. Sci., g_,. (1), 1 (1953).
96
(16) Eckert, E.R.,G. and Drake, R. M., Jr., Introduction ~ the Transfer of Heat !!!£ Mass, McGraw-Hill, New York (1950).
(17) Foresti, R., Jr., and Liu, T., "How to Measure Power Requirements for Agitation of Non-Newtonian Liq,uids in the laminar Region," Ind. and Eng. Chem., .21 (7), 860 (July 1959).
(18) Gray, J.B., "Batch Mixing of Viscous Liquids," Chem. Eng. Prog., ~ (3), 55 (March 1963).
(19). Harriott,lo,. "Heat Transfer in Scraped-Surface Heat E:x:changers, 1'
Chem. Eng. Prog. Sym.p. Series, 22., (20), 137 (1959).
(20) Hoogendoorn, C. J. and den Hartog., A. P., "Symposium: Hanteren Van Viskeuze Vloeistoffen - Deel 1. Storming En Merging Van Viskeuze Vloeistoffen: VI. Modelstudies Aan Roerders in Het Re-gebied Van 0.10 to 1,000," De Ingenieur - Chemische Techniek, Jrg. 77, Nr. 17, ch 37 (23 April 1965).
(21) Huggins, F. E., "Effects of Scrapers on Heating, Cooling, and Mixing," Ind. and Eng. Chem., 23, (7), 749 (1931),
(22) Houlton, H. G., "Heat Transfer in the Votator," Ibid • .2.2., (6), 522 (1944).
(23) Jepson, c. H., "Future Eictrusion Studies," Ibid., 45, (5), 992 (1953).
(24) Kapustin, A. S., "Investigations of Heat E:x:change in Agitated i Vessels Working with Viscous Liquids, 11 Int'. Chem. Eng., 3,
(4), 12i (1963). -
(25) IG.inkenberg, I. A., "Residence Time Distributions and .Axial Spreading in F1ow Systems," Trans. Instn. Chem. Engrs., frl, (1), T141 (1965).
(26) Kool., J., "Heat Transfer in Scraped Vessels and Pipes Handling Viscous Ll.quids," Trans. Instn. Chem. Engrs., 36, 253 (1958).
(27) Iatinen, G. A., "Discussion of Correlation of Scraped Film Heat Transfer in the Votator, 11 Chem. Eng. ,Sci~, 9,. (33}, 26.3 , (1959).
(28)
(29)
(30)
(31)
(32)
(33)
· (34)
(35)
(36)
(37) ~
(3$)
(39)
(40)
(41)
(42)
Iaughlin, H. G., "Data on Evaporation and Drying in a Jacketed Kettle," Trans. Am. Inst. Ch.em. Eng., 36, 345 (1940).
Levenspiel, O., Chemical Reaction Engineering, John Wiley and Sons, Inc. New York (1962). ·
Li, N. N., and Ziegler, E. N., "Effect of Axial Mixing on Mass Transfer in Ex:traction Colurrms," Ind. and Eng. Chem., 59, (3), 30 (1967).
97
Mixon, F. O., Whitaker, D. R. and Orcutt, J. C., "Axial Dispersion and Heat Transfer in Liquid-Liquid Spray Towers, 11 A.I. Ch •. E. J., 1:1, (1), 21 (1967).
Miyauchi, T. and Vermeulen, T., "Longitudinal Dispersion in TwoPhase Continuous-Flow Operations," Ind. and Eng. Chem. Funds.·, g_, (2), 113 (1963_).
Miyauchi, T., AEC Rept. UCL-3911 (Aug. 1957) and supplement with Vermeulen, T. and McMullen, A. K., (Jan. 1958).
Na.gate, S. , Yanagimoto, M., and Yokoyama, T., "A Study of Mixing of Highly Viscous Liquids, 11 Chem. Eng. (Japan) 21, (5), 278~286 (1957).
Oldshue, J. Y. "Annual Review - Mixing," Ind. and Eng. Chem., 2§, (11), 50 (1966).
Penney, W.R. and Bell, K. J., "Close-Clearance Agitators: Part I - Power Requirements; Part II - Heat Transfer Coefficients, 11
Ind. and Eng. Chem. 59, (4) 39 (1967). See~, No. 6 for legend on Figure 7 which ~s left off in article.
Penney, W. R • ., "The Spiralator - Initial Tests and Correlations,." A.I.Ch.E. preprint 16, Eighth Natl. Heat Transfer Conf., Los Angeles, Calif, (August 1965).
Skelland, A.H. P., "Correlation of Scraped-Film Heat Transfer in the Votator," Chem. Eng. Sci., 7, 166 (1958).
Skelland, A.H. P., 11Scaleup Relationships for Heat Transfer in the Votator," Brit. Chem. Eng., 2., (6), 325 (1958).
Skelland, A.H. P.~ Oliver, D.R. and Tooke, s., "Heat Transfer in a Water-Cooled Scraped-Surface Heat Ex:changer, 11 Brit. Chem. Eng., 1, (5), 346 (1962).
Sleicher, C. A., Jr. , "Axial Mixing and Ex:traction Eff:i.ciency, 11
A.I.Ch.E. J., z, (2), 1~5 (1959).
Squires, P.H., "Screw Ex:trusion - Flow Patterns q.nd Recent Theoretical Developments, 11 SPE Trans. , 7 ( January 1964) •
98
(43) Taylor, G. I., "Dispersion of Soluble Matter :in a Solvent Flowing Slowly Through a Tube, " Proc • Roy. Soc., 219A, 186 (1953) ..
(44) Taylor, G. I., 11The Dispersion of Matter :in Turbulent Flow Through a Pipe," Ibid., 223A, 446 (1954).
(45) Uhl, V. W. and Root, W. L. Ill, "Heat Transfer to Granular Solids · :in Agitated Units,"Chem. Eng. Prog., .§.1, (7), 81 (1967)0
(46) Uhl, V. W. and Gray, J. B. (Editors), Mixing - Theory: !!!S Practice, Academic Press, New York (1966).
(47)
(48)
(49)
(50)
Uhl, V. W., · "Heat Transfer to Viscous Materials :in Jacketed Agitated Kettles," Chem. Eng. Prog. Symp. Series, .iL (17), 9.3 (1955).
Uhl, V. Wo and Vozniok, H. P. 11The Anchor Agitator, 11 Chem. Eng. Prog., 2.2., (.3), 72 (1960). . ·
Wehner, J. F. and Wilhelm, R.H., "Boundary Conditions of Flow Reactor," Chem. Eng. Sci., .2., (1), 89 (1956).
Young, E. F., "New Tool Analyzes Mixing Stages," Chem. Ehg., 2Ji, 241 (February 1957).
a
c
c
d
D
J}E
g
NOMENCLATURE
Nomenclature for Main Body of Thesis
- parameter defined by equation (A-10)
- inside surface area. of heat exchanger, sq. ft.
- surface-area of agitator, sq. ft.
- cross-sectional area of flow channel, sq. ft.
- cross-sectional area. of exchanger wall, sq. ft.
- clearance between agitator and vessel wall, ft.
- specific heat at constant pressure, B.t.u./lb.m F.
- diameter of agitator, ft.
- diameter of vessel, ft.
- equivalent flow channel diameter, ft.
- diameter of inner shaft, ft.
- effective diffusivity of mass in the dispersion model, sq. :rt./hr.
- parameter defined by equation (A-14)
gc - conversion constant, 32.2 lb.m-ft./lb.rsq. sec.
h - heat transfer coefficient, B.t.u./hr. sq. ft. F
h - pitch of helix on auger or helical ribbon, ft.
k - thermal conductivity, B.t.u./hr. rt. F.
- effective thermal conductivity in the dispersion model, B.t.u./hr.ft. F. . ·
L - length of agitator, ft.
LMTD - logarithmic mean temperature difference, F.
99
100
MTD - mean temperature difference, F.
nb - nurober of blades on agitator
N - agitator speed, rev/hr.
Nu - hD/k, Nusselt No.
p - power, ft.-lb.f/sec.
Pb - power consumed in the bulk of the fluid, ft.-lb.f/sec.
Pc - power consumed in the clearance, ft.-lb.f/sec.
pt - Pb+ Pc, total power consumed by straight agitator, ft.-lb.f/ sec.
P - perimeter of flow channel,ft.
P - conventional power numb.er, ptgc4°N3d5
pbL - Pbgc/fN3d4L
PcL - Pcgc/frPd4L
PtL - ptgc/fN3d4L
Pe
Pr
Re
t
- V L , Peclet number for axial dispersion -°'=; . - ~c , Prandtl number
le - heat flux to the fluid from the inner heat exchanger wall,
Btu/hr, sq. ft.
- heat fl\lJC from the electrical wall heating element, Btu/hr. sq, ft.
- Nd2;LJ/~, rotational Reynolds number
- ~ , axial flow Reynolds number
- circumferential thickness of agitator nearest vessel wall, ft.
T · - temperature, F.
U - axial flow velocity, ft./hr.
u - overall heat transfer coefficient, Btu/hr. sq. ft. F.
vt - blade tip velocity, ft./hr.
W - axial flow rate, lb. m./hr.
y ft;_
z - axial dimension, ft.
Wa - width of agitator arm, ft.
Wr - width of helical ribbon, ft.
Greek Letters
~ - constant in equation (2-10)
oC - proportionality constant
~ - exponent on Pr in equation (2-10)
- tv,_4- , number of transfer units for the heat exchanger
- ~.l?iie , number of transfer units for the agitator We.-
- time between successive scrapings (contact time), hr.
?;- ~· , temperature jump ratio 72- 7i:
@
~ - kinematic viscosity, lb.m./hr.ft.
- absolute viscosity, sq. ft./hr.
- kinematic viscosity, lb.m./hr.ft.
-: liquid density, lb.m./cu.ft.
- ratio of bulk to surface viscosity
~-Tw ( ) , parameter defined by equation A-3 'Ji,·- Tw
/I/J 7 ,o , ratio of the mean temperature difference to the Ll,/17.J:?
logarithmic mean temperature differ~nce
Subscripts
0 - at z :;::: 0 just inside the exchanger inlet
A - agitator
b - bulk liquid
E - signifies effective thermal diffusivity of heat or mass
F - fluid
H - heater
101
102
i - exchanger inlet
L - at z = L, the ex.changer .outlet
w - exchanger wall
Nomenclature for Data Reduction Computer Programs
Inp~t De.ta
AMPS - electri>cal current through the exchanger wall heating element, amperes
OIS - cycle timer reading at the start of a timing period
OIF - cycle ti.mer reading· at the end of a timing period
NW - the number (or numbers if NW is two or three digits) of weight or weights on the dynamometer lever arm
POT - setting of the potentiometer speed control for the D.Co motor which turned the agitator
TI - time interval between the start and end of a cycle timer timing period, seconds
T,FLOW - time for the test liquid to rise six inches in the reservoir, seconds
TMI - month in which data were taken
TMD - day in which data wa;re tal(en
TMZ - time of day in minutes from 12 p.m. in which data were taken
TWMV - 1 x 11 array of the eleven wall temperatures, millivolts
TEOIMV - temperatu:re in the exchanger outlet line, millivolts
TEILMV - temperature in the exchanger inlet line, millivolts
TEIMV - temperature just inside the exchanger at the inlet end, milli:voJ..ts
TEOMV - temperature just inside the exchanger at the outlet end, millivolts
VOLTS - voltage drop across the exchanger wall heating element, volts
XLA. - distance from the side of.the weight nearest the D.C. agitator motor ·'to '.£he frame of 'the ag1tator motor, inches
103
Calculated and Program Variables*
AGRPM - N, rev./rrrln.
BETA - hA/wc; number of·· tra.nsf el'! :units for the heat exchanger
BR - Br:inlona.n number, ratio pf power input to the·test liquid by the agitator to power input to the test liquid through the heat exchanger wall
C - c, heat capacity of the test fluid at the average film temperature
DA - d, ft.
DELTE - TL - Ti
DELTF - (Tw - Tb)z = 14
DENB . - p, test fluid density at (Tb)z == 14
HP
HC
HX
I
L
M
p
PE
PEDA
PN
Q
Q
- net horsepower the agitator imparted to the test liquid
- h1 experimental heat transfer coefficient at z = ,14 corrected for a.xia.l wall heat conduction
- experimental heat transfer coefficient uncorrected for axial wall heat conduction
- loop counter
= loop counter
- :ind:ex to identify agitator diameter
- inside circumference of the test heat exchanger, ft.
-.JlJ. , Pe
°"'• - 2r,t C>".-De
- pbL
- electri·cal heat inPQ.t to the wall heating element, Btu/hr.
- net heat inp,J.t to the fluid through the exchanger wall, Btu/hr.
. i*J'ot all these variables will be identified; only those essential
to easily comprehending the calculation procedures will be identified. Where applicable these variables shall be identified in terms of the nomenclature of the main body of the thesis.
•
QAGIT - power input to the test.liq,uid by the agitator, Btu.,'hr.
QL - heat loss from the heat exchanger to the laboratory environment. Btu./hr.
- qF/qH (see equation (E-2))
104
QOAR
QOA - average heat nux from the inside exchanger wall to the test fluid, Btu./hr.sq.ft.
REA
RER
RERC
T
T
TEAVG
TEI
TEIL
TEO
TEOL
TF
- Re · a
-r x Re, Reynolds number based on blade tip velocity
- Re
- total torque produced by the agitator, in.lb.£.
- (T-TF) net torque produced by the agitator acting on the test liquid, in. lb. f. ·
- (Tb)z = 14
- To
- T, .1
= TL
- T1
- torque produced by the agitator due to bearing friction, in. lb •. f.
'!'FILM .{ii:i}.,.,.., average fib! tempe~ture, F
TB.A.TIO - ~ :_ T,: - , temperature jump ratio ~
TWA VG . - ~ rwul){. , average wall temperature, F
-N•, ., r1vf# J t: r""5J TWM L
TW(N) = 1 x 11 array of the eleven wall temperatures, F
VAT - Vt
VFPM - axial flow velocity, ft./min.
VISB ~,JI., test fluid kinematic viscosity at (Tb)z = 14
Wl - weight of dyna.JD.C>m~ter weight niµnber ·1, lb.m.
k.mt - w
XJVISC -
XK
XNU
XL
- k, test fluid thermal conductivity at the average film temperature
hd ~-'~-1 T' ,.,_ - length of the test heat exchanger, ft.
105
APPENDIX A
ANALYTICAL SOLUTIONS OF THE DISPERSION MODEL
There were two objectives of the following mathematical work:
The first .was to obtain dispersion parameters from the experimental
data. The second was to develop a method for conveniently pre4icting
the MTD in an exchanger with axial dispersion.
The solutions obtained were the minimum necessary to achieve
these objectives, Considerably more theoretical work could have been
done. Much numerical differential equation solving could have been
done. In particular numerical methods could have been used to solve
the dispersion model with an axial variation of heat transfer coeffi
cient. It was decided, however, to use the analytical solutions .to
their fullest extent here and then let future researchers use this
work to guide their work, which may well include numerical work.
Analytical solutions for the dispersion model were obtain~d for
the following special cases:
(1) constant wall temperature with no axial dispersion in the inlet
and outlet lines. This solution was originally given by
Danckwerts (15). It is recast in heat transfer terminology here.
Wehner and Wilhelm (49) have shown that the axial dispersion in if the inlet and outlet lines does not affect the temper~ture
distribution in the exchanger.
(2) constant wall heat flux with no dispersion in the inlet and outlet
106
107
lines.
(3) constant wall heat flux with no dispersion in the inlet and outlet
lines and with infinite axial conduction in the agitator (i.e.
the thermal conductivity of the agitator is infinite) •.
Constant Wall Temperature with A,xial Dispersion
In the Inlet and Outlet Lines
Development of Basic Differential Equations
The sketch below shows qualitatively the temperature distribution
in the exchanger,
·-~----~72
0 L
The governing differential equation is developing by making a
heat bala~ce on a differential element of the heat exchanger. The
following sketch gives.the heat streams associated with an axial
differential element of the exchanger.
hPdc CTw-Tt,)
Wclb ~
!i{Wc 7;,)cl.a-
The differential element is at steady state, therefore:
Heat In - Heat Out = O
This heat balance then b~comes
J.. .,, d n ,~/ d~ ( . ) ~ nFd z. - WC - - 'h? ~- ~
~ cl&
because Tb is the only dependent variable.
Let
'I -... Then equation (A-2) beQomes
J.?e,4F ~ WcL dyz..
d¢ dy
hPL /19 _ 0 \I\IC r..r
108
(A-1)
(A,,-2)
(A-3)
(A-4)
(A-5)
Now
ke/t,c I J ::;:-
tW) L -}1\/cL L))_
?~ ( Re ) o<l=. ~c
Let
~= hPL h/J
- We we Then equation (A-5) becomes
J ,-Pe
General Solution
def> - ;61¢ dy
The general solution to equation (A-8) is:
109
) - Pe (A-6)
(A-7)
- t:) (A-8)
/1) ::- Al ?f {/1°4 )'/ . 11 / /£ {/~) y <f' /VI e f- /Vz.. e (A-9)
where
a == I ;,,. (A-10)
Boundary Conditions
The two necessary boundary conditions are obtained by making heat
balances at Y = 0 and Y.= 1. For the case considered here of no
dispersion in the inlet and outlet line these two boundary conditions
.were first given by Danckwerts (15). The two boundary conditions are
as follows:
/ ldrl>] ~ dY y:o
(A~ll)
110
= 0 (A-12)
Particular Solution
Application of these boundary conditions to equation (A-9) gives
the following particular solution:
where
(A-14)
0-~· Rea,rranging Particular Solution to Have ;:r _ 72 as Dependent Variable
The theoretical development in the preceding section was for the
condition of constant wall temperature. The experimental wall tempera-
ture is not constant. Also because of axial conduction in the exchanger
wall the wall temperature is not linear in the axial direction as
would be obtained if the heat flux to the test fluid and the heat
transfer coefficient were constant. Due to conduction from the ex-
changer wall to the endplates the axial variation of exchanger wall
temperature· cannot be described analytically. The approach, which will
be used here to develop an analytical method for determining C<"..c from
experimental data, is to eliminate Tw from the analytical solutions for
the cases of constant wall temperature and constant heat flux and show
that when/1= 0 the solutions for these two limiting cases coincide.
This limiting solution will be used to obtain C>'E from experimental
data.·
111
With this in mind let us rearrange the particular solution to
contain temperatures ~hich are readily determined experimentally.· The
particular solution given as equation (A-13) can be rearranged as
follows:
7;-7; 7;-7;:
is only a. function of Pe and ~
graphically in Figure 25.
This relationship is presented
Ratio of MTD to LMTD
The ratio of MTD to IMTD (MTD/LMTD =G) has been used extensively
for design of heat exchangers. It has been selected as a design para-. . ' meter here, Other dimensionless parameters involving the same tempera-
tures as ~ could have been used, It was felt that € would have more
physical meaning to a designer than other parameters which could have been used,
The LMTD can be expressed as follows:
LMTD ~ -(~-~) {;A-1)
Ln {¢~) (A-15)
The MTD can be calculated by integrating (Tw - Tb) over the
length of the exchanger
(A-16)
Substituting for(/> from equation (A-13) equation (A-16) becomes
I
MTD = - 72- r... }Ji,,,>e ~ t,, .... y.,~(/-4)e f't,,.,.,,,.~<A-1 ?J
112.
After simplifying we obtain
c,;· -r..,J{ 6 - l) NliD = ~ (A-18)
Then
Ii= = -~ (A-19)
Thus , is only a function of Pe and,8. This relationship has
been plotted in Figure 31:.
All the theoretical work here has been done with Tw ·and h. The
mathematical development is exactl~ the same if Tw is replaced by Tc
and h with the overall heat transfer coefficient. Thus Figure 30 ca,n
be used for design purposes, using~ in conjunction with h or Tc :in
conjunction with u.
Constant Heat Flux With No Dispersion
in the Inlet and Outlet Lines
Develo:ement Of Ba.sic Differential Equation
For this case the basic/ differential equation, wbich is ·&nalogrns ii
to equation (A-2) is as follows:
(A-20)
Let
(A-21)
11.3
%crt = R (A-22)
then equation (A-20) becomes
- (A-2.3)
Gen;ra1 solution
The general solution to equation (A-22) is a.s follows:
(A-2.3)
Boundary Conditions
The two necessary boundary conditions are analogous to those for
the constant wa.11 temperature case,; thus, with ;> replaced by ..._they .
· are given as equations (A~11) and (A-12).
Particular SolJ.,tion
Application of these boundary conditions·to equation (A-2.3) gives
the fallowing particular solution
(A-24)
. 1-12 Rearranging Particular Solution to Have · ~ _ 7t as Dependent Variable
The following relationship is obtained by evaluating equation
(A-.24) at z = L.
R -~) -6% -= -~ l1- e -1-/ (A-25)
but
R .. o/w~~· (7i-h9 Yn (A-26)
114
Thus.equation (A-25) can be rearranged as follows:
= ---"'!~--£1 -e -~] (A-27)
];;-?;· Note that
4-7,.e _constant wall temperature
is only a function of Pe; whereas, for the
case ?~ -'J;: is a function of both Pe and 7.t- it·
~· The relationship of equation (A-27) is presented graphically in
. Z"-7+· Figure 25. The relationship between '"7"' "9"l and Be for the case of
~L - ,,:
constant heat flux is exactly the same as .the relationship between
7;-~· and Pe for the constant wall temperature case with,'f = O. 7i. - ?;: ' The experimental conditions of· this investigatio;n are neither constant
heat flux nor co~stant wall temperature. Figure 25 indicates that
testing should be· conducted with small values of ~ in order for the
experimentally determined values of <">'-.: to be physically meaningful.
Constant Heat Flux with Infinite Conduction
in the Agitator and No .Dispersion
in the Inlet and Outlet Lines
Development of Ba.sic Differential Equation
With infinite conduction in the agitator (i.e. kA is infinite)
the temperature of the agitator is constant throughout.
The governing differential equation is developed by ma.king a heat
balance on a differential element of the heat exchanger. The following
sketch gives the heat streams associated with an axial differential
element 0f the exchanger.
115
,t,11 C.i ... Z}Jr:
. -44:jf j4Jli{-~ l;::j )Ji:
A steady-;:itate heat balance on the differential fluid element
yields the .following di.f'.f'erential equation:
Let
J.,1; 41-Wc =
:%',,01;· then equation (A-28) becomes
(A-29)
(A-30)
(A-31)
(A-32)
Let
then equation (A-33) becomes
/ d z.1/ -R! d yz General Solution
dtr dY
The gener~l solution to equation (A-35) is as follows:
&(1;a') y ft. {I-a ')y. (j)= N5 e z.. ·. -1-~·e z
where
a I -
Boundary Conditions
p..~I Pe
?
116
(A-34)
(A-35)
(A-36)
(A-37)
The two neQessary boundary conditions are analogous to those for
the constant wall temperat~re case which are given as equations (A-11)
and (A-12). These boundary conditions in terms of~ are as follows:
~ lddyt/] : ~ -I- (/>,4 f- _L -/ (A-38) ,-e Y ;;o (.) 41
0 (A-39)
Particular Solution
Application of these boundary conditions to equation (A-36) gives
the following particular solution:
(A-40)
117
where
(A-41)
)< )- C,4 - (A-1.+2)
Determination of TA
Now
(A-34)
~ { % ) has to be determined. t can be determined from the,
condition that all heat which enters the agitator must leave the
agitator because no heat is stored or generated in the agitator.
Mathematically this condition can be expressed as follow$:
(A-43)
In terms of ~ the above equation becomes
(A-44)
t/J11 can be determined from equation (A-44) after substituting for
(f from equation (A-40) and integrating between limits. ~ is as
follows:
® - {I- 4,)-}- If I-Fl
(A-45)
where
F' - (A-46)
118
Rearranging Particular Solution to Have 0- 7'• as Dependent V~:r:~Jible
4-'i After substituting for~ from equation (A-45) equation (A-40)
can be rearranged as follows:
, /7, ff. ' - ,e,. ,7 I Z-7;: = .11_ll-l6')e-z 411 -«-"'') e e. .J -72-Tc· - Zt:1'8' ~~ -I . I
(A-47)
This equation is exactly the same as equation (A-14) for the
constant wall temperature case with a 1 and g' replaced with a and g.
Now a = a' and g = g' if / =~ ' • Now .
~= _hPL. - 1i,. -We Wt! (A-7)
,t' :a h,1/l. L - h~ - We - We::. (A-31)
thus/ =,41 if hP = hAPA, It is logical to assume h = hA but P,;;r,/ PA,
In fact
21)
"'lf"O
thus ;S 1 ~ 0,64,4 ,
Then for constant heat flux the effect of infinite agitator
conduction will be less than if the wall temperature were constant.
And further the agitator conductivity is finite; therefore, the effect
of agitator conduction will be even less than equation (A-47) predicts.
li-~ It should be noted that the relationship between , Ilia · and
~I and Pe is presented in Figure 24. ~·~*
To sunnnarize briefly, the effect of agitator conduction will not
influence the calculated values of C>teif testing is conducted at
sufficiently small values of;!/'.
AP:PENDIX B
.. THERMOCOtrPLE CALIBM TIONS
The eleven wall thermocouples and the exchanger inlet line (pump
outlet line) and exchanger outlet line thermocouples (thermocouples
. 1 thru 13 on Figure 3) were constructed from 30 gauge, teflon-covered
iron-constantan wires. The thermocouple junctions were made with a
mercury-bath thermocouple welder. These thermocouples were made of
consecutive lengths from a roll of constantan thermocouple wire. The
exchanger·inlet and exchanger outlet thermocouples (thermocouples 14
thru 15 on Figure 3) were purchased from the Conax Company, Buffalo,
New York. They were made of 30 gauge iron-constantan thermocouple wires
in a 1/16 inch diameter stainless-steel sheath.
The above-mentioned fifteen thermocouples were calibrated in.the
Research and Development laboratories of Phillips Petroleum Company.
The calibration was performed in a constant-temperature silicone-oil
bath. The bath container was an uninsulated, open-top, two-quart
Dewar flask. The bath temperature was controlled by a thermistor
temperature controller,
The calibration potentiometer was a Minneapolis-Honeywell model
2781 with a Minneapolis-Honeywell model 3117 spotlight galvanometer.
The calibration procedure was to start the readings immediately
after cutoff of the control heater and take the readings as the bath
cooled down. At all calibration temperatures a set of readings was
119
taken going from thermocouple 1 to thermocouple 15 and then a set of
read:i,ngs was taken going from thermocouple 15 to thermocouple 1.
120
The thermocouples were calibrated against mercury-in-glass
thermometers. The specifications of these thermometers are as follows:
The thermometers for 100 F and 200 F were manufactured by the Precision
. Thermometer and Instrument Company, Southhampton, Pennsylvanie,. The
smallest graduation was 0.05 F. The serial numbers were 714381 and
72321~ respectively. The reference thermometer for 130 F and 160 F
were ASTM Kinematic Viscosity, graduated in 0.1 F, and ASTM Paraffin
Melting Point, graduated in 0.2 F, respectively. They were manufactured
by the Taylor Company, Rochester, New York, The serial numbers were
2320641 and 4192122, respectively.
The calibrations are given in Table I.
\)> ... TABLE I
THERMOCOUPLE CALIBRATIONS
Reference Thermometer 103 103 103 131.5 131.25 164.25
1 2.0339 2.0339 2.0281 2.8579 2 .. 8525 3.8320 2 2.0332 . 2.0332 2.0271 2.8580 2.8512 3.8316 3· 2.0340 2 .. 0340 2.0284 2.8586 2.8539 3 .8326 4 2.0340 2.032.9 2.0281 2.8583 2.8531 3.8314 5 2.0326 2.0326 . 2 .0278 2.8585 2 • .8524 3 .8300 6 2.0327 . 2 .0319 2.0285 2.8586 2.8534 3.8295 7 . 2 .0327 2 .• 0322 2.0284 2.8591 2.8541 3.8305 8 2.0327 .2.0315 2 .0.290 2.8581 2.8541 3.8296 9 .2.0327 2 .0309 · 2~0284 2.8586 , 2.13546 -3 • .8321
10 . 2.0325 2 .0309 2.0289. 2 • .8581 2.8553 3.8305 11 2 .0325 2.0296 2.0284 2.8588 2.8561 3.8265 12 2.0320 2.0289 2.0266 2.8556 2.8525 3.8229 13 2.0320 · 2 .0292 2.0274 ·2.8557 2.8530 3.8255 14 2.0272 2.0234 2.0224 · ,2.8406 . 2.8388 3.8026
.15 2.0.250 2.0221 2.0232 2.8386 2.8376 3.8025
* * ** * ·** *
' .. * Readings taken from. thermocouple 1 to 15 ** ·Readings taken from thermocot.1ple·l5 to 1
164.2 205.63
3.8255 5.0885 3.8270 5.0895 3 .8314 5.0934 3.8309 5.0929 3.8292 5.0961 3 .8311 5.0946 3.8329 5.0956 3 .8318 5.0965 3.13331 5.0979 3 .. .8331 5.0985 3 .• 8332 . 5.0979 3 .. 8265 5.0931 3.8281 5.0943 3.8084 5.0560
· 3.8105 5.0580
** *
2·05. 73
5.0950 ,5.0960 5.0995 5.0979 5.0975 5.1000
,5 .. 0999 5.0996 5.1004 5 .• 1011
. 5.0999 5.0941 5.0942
· 5.0562 5.0580 . **
206.13
· 5.1060 5.1075 5.1110
. 5.1095 5.1072 5.10.85 5.1094 5.1100
. 5 .• 1095 5.1107
. 5.1088 5.1029 5.1034 5.0665 5 .• 0655
*
I-" I:\) I-'
APPENDIX C
TEST FLUID PHYSICAL PROPERTIES
Physical Properties of Ethylene Glycol
Heat Capacity and Thermal Cond~ctivity
The heat capacity and ther;mal conductivity data at atmospheric
pressure were take:n. from the Union Carbide Booklet number F-4763G, enth
tled 11 Glycols."
The heat capacity and thermal conductivity were curve-fitted by
hand as linear functions of temperature. The result:1,ng functions are as
follows:
c = 0.517 + 0.0006T
k = 0.186 = .000249T
( C-'1)
(C-2)
The rna.ximum error between 80 F and 180 F was less than ·0.3 percent
for heat capacity and less tha~ 0.4 percent for thermal conductivity.
Density
The density data were taken from both Union Carbide Booklet number
F-476JG and from Eckert and Drake (16). The density was also hand
curve-fitted as a linear function of temper&ture. The resulting func
tional is as follows~
;L) = 71.2545 - 0.02515 T (C-3)
122
123
This curve fit is approximately 0.2 percept below the best straight
line (a straight line fits the data as well as any other curve would
fit the data) through the data from Ecker~ and Prake (16) a~d approxi
mately 0.2 percent above the best.straight line through the data from
the booklet entitled "Glycols."
Viscosity
The viscosity data were also taken from Eckert an~ Drake (16) and
from Union Carbide Booklet number F-4763G. The logarithm of viscosity
was plotted vs. temperature and a smooth curve was drawn through the
data. Data from both sources deviated a maximum of 3 percent from the
smooth curve. This smooth curve was curve-fitted by regression analysis
on a digital computer. The viscosity and temperature were entjered into
the computer at 5 F intervals from the smooth curve. The resulting
curve fit is as follows (viscosity in centipoises):
ll'l(µ) = 5;175S9 - 0.03~22136T + 0.0001134165T2 - O.OOOOQ01463195T3
(C-4)
The largest error in the curve fit between SO F and lSO F was
0.61 percent at 110 F.
Physical Properties of Gulf Harmony Oil 151
The physical properties of Gulf Harmony Oil 151 were obtained
from Mr. R~ T. Kern, Jr., Staff Engineer, Gulf Research and Development
Company, Marketing Technical Division, P.O. Drawer 203S, Pittsburgh,
Pennsylvania.
The physical properties supplied by Mr, Kern a:re given in Table
124
The heat capacity, thermal conductivity and density data were hand.
curve-fitted as linear f-q.nctions of temperature. The resulting func-
tionals as as follows:
c(Btu/lbF) = 0.402 + 0.000586T (C-5)
k(Btu/hrftF) = 0,0761 - 0.0000226T
f (lb/ft3) = 58.03 ,.. 0.03413'.I' (C-7)
The maximum errors in these curve fits are 0.65 percent for
specific heat, 0.28 percent for thermal conductivity and 0,43 percent
for density.
The viscosity data were plotted as viscosity in centistokes vs.
temperature on an A.S.T.M. Standard Viscosity-Temperature Chart for
Liquid Petroleum Products (D341). All data points were within 3 per-
cent of a straight line.
The viscof;)ity was determined at 100 F and 2:j.(tl F in the Research
and Development laboratories of Phillips Petroleum Company, Bartlesville,
Oklahoma (Phillips Research Notebook 14401-6). The viscosity -was 517.1
centistokes at 100 F and 31.88 cent;istokes at 210 F. These data are
within 3 percent of the straight line through the data supplied by Mr.
Kern. This straight line relationship on the A.S.T.M. viscosity paper
was curve-fitted by regression analysis on a digital computer. The
viscosity and temperature were entered into the computer at 5 F :inter-
vals from the smooth curve. The resulting curve fit is as follows
(viscosity in centistokes):
Log(}() = 11. 79908 - 0,07765l74T + 0~0002598J15T2 - 0.000000377051T3
(C-8)
125
The largest error in the curve fit was. 1.48 percent at 105 F.
TABLE II
PHYSICAL PROPERTIES OF GULF HARMONY OIL 151
Temp. Viscosity Density Thermal Specific ( F) (Saybolt Universal (gm/cc) Conductivity Heat
Seconds) (Btu/hr/sq ft/F/~) (Btu/lb/F)
50 23,000 0.8993 0.90 0.433
100 2,520 0.8764 0.89 0.457
150 545 0.8518 0.87 0.490
200 183 Q.8176 0.86 0.519
APPENDIX D
EXPERIMENTAL AND REDUCED DATA
Both heat transfer and power requirement data were reduced on the
IBM 7094 digital computer.
The FORTRAN listing of the computer program to reduce the data
fr0m the heat transfer experiments is given in Table III.
The FORTRAN listing of the computer program to reduce the data
from the agitator power requirement experiments is given ih Table IV.
The computer program nomenclature is given in the NOMENCLATURE
section immedia:t.ely after the nomenclature for the ma.in body of the
thesis.
Ex:perimenta.l and reduced data. from the heat transfer tests as
output from the computer a.re presented for the tests with Gulf Harmony
Oil 151 as the test liquid for the 3 .500, 3 .$31~ 4.000 and 4.039 inch
diameter blades in. Tables V, VI, VII and VIII, respectively. Such data
for the tests with ethylene glycol for the 4.000 inch diameter blade
a.re presented in Table IX.
Experimental and reduced data from the agitator power requirement
tests as output from the computer are presented for the tests with
Gulf Harmony Oil 151 as the test liquid for the 3 .500, 3. 8.31, 4.000
and 4.039 inch diameter blades in Tables X, XI, XII and XIII,
respectively.
126
TABLE III
FORTRAN STATEMENTS FOR HEAT TRANSFER DATA REDUCTION PROGRAM $IBFTC M•IN NOOECK
DIMENSION TW~V(lll, TW(ll), WRIT(15,26l 1 WROT(15,211 DJ"IENSIDN NR"A(4), OAIA(4 I
C CURVE FIT IRON-CONSTANTIN THERMOCOUPLE TABL~S IN OfG. F VS. MV TEMP(A) = 32.36685 + 135.329 • (-.2902632 + (.011734 - .00015831
l*Al*Al*Al*A C PHYSICAL PROPERTIES - ENGLISH UNITS EXCEPT ET~YLENE GLYCOL VISCOSITY C CtNTIPOISES ANO OIL VISCOSITY IN CENTISTOKES
XCIAI= .402 + .030586 *B XXKICI= .0761 - .0000226 *C DENIDI = 58.03 - .03413 * ~ VIS(E) = 2.71828183 ** (ll.79908 + (-.07765174 + !.000259831S -
1 .000000377051 * El * Fl * fl Wl = 241.5 I 453.6 W2 = 405.5 I 453.6 W3 = 551.0 I 453.6 OAl = 3.500 DAIA(4l = 4.039 1)1>.IA ( 31 = 4. 000 DA I A I 2 I = 3. q31 OA!A<l I = 3.500 P = 3.1416 * 4.058 I 12.0 XL= 21.75 I 12.0 I = 0 l.PC = 0 D = 4.058 I l;?.O • ., = 1 .
141 CONTINUE l. = 0
l ~EAO 15,100) TMl,TMD,TM2,TdMV,TEOLMV,TEILMV,TEIMV,TEOMV,VOLTS, lA~PS,CIS,CIF,Tl,TFLOW,?OT,NW,XLA
100 FORMAT (A5,Al,A4,14F5.3/F5.3,2F5.2,3F5.0,F5.2,F5.1,15,F5.21 I = I t l L = L + l DAI = DAIAIMl DA = DA.I I 12.0 DO 3 N = 1,11 TW'1V'J = TWMVINI
3 TWIN) = TEMP(TWMVNl TEil = TEMP(TEILMVJ TEOL = TfMP(TEDLMVl TEI = TEMPITEIMVJ + O.~ T~O = TcMPITEOMVl + a.~ TWAVG = 0,0 DO 5 N=l,11 TWAVG = TWIN) I 11. + TWAVG TW". = IH114l t TW(51 I I 2.0 TEAVG = (14.0/27.0l*TEOL + (8.0/22,0l*TEI DELTF = TWM - TEAVG DELTF = TEOL - TFIL I)') 119 ~ = l ,2 TFILM = !HIM + TEAVGl I 2.0
C PHYSICAL PROPERTIES XK =XXKI TF IL Ml C =XCITFILMl
OENB = DEN!TEAVGI !)<NW = JJEN(TWMI DENWA = DEN(TWAVGI VISB = VIS(TEAVGI * OENB * 2.42 I 62.4 VISWM • VIS(TijMJ * DtNW * 2,42 I 62.4 VISWA = VISITWAVGl *DtNWA * 2.42 I 62.4 V!SR = V!SB I V!SWM
C Hf.4T FLUX Q =VOLTS* AMPS* 3.41304 QL = (0.464 + 0.0019*1TW{41 - 72,0ll * ITW14l - 72,0) Q = Q - QL Q•JA = Q I 1. 9256 QOAR = 1.0 + (4,014/0l*(TWl31 t TW(6l - T~l4l - TW(5ll*36,0/2.0
C FLOW PARAMATERS (MEASURED VOL 184 CU IN .2225 CU FT l.&7 GALl WLBH = .2225 * 3600. * DENITEOLI I TFLOW KEh = 4.0 * wlRH I 13.1416 *D*VISB l VFP~ = .2225 * 60. I 13.1416 *D *DI 4. * TFLOW l AGRPM = 6.11 * (CIF -ClSI I Tl VU = I 3.1416 *DA * AGRPMI I 60. RFR =VAT* 3600. *DA* DFNB I V!S8 R~QC = RER I 3.1416
C POWEO IF IXLA.LT •• 051 GO TO 18 IF (K,fQ.21 GO TO 74 XLA = XLA + 4.75 IF (NW.EQ.11 GO TO 11 IF ·1 NW,EQ. 21 GO TO 12 IF INW.EQ.31 GO TO 13 JF (NW.EQ.12) GO TO 14 !F (NW.EQ,131 GO TO 15 IF INW.EQ.231 GO TO 16
11 T = Wl * (XLA + ,1131 GO TO l7
12 T= W2 * IXLA + ,186 I GO TO 17
13 T = W3 * (XLA t .2571 GO TO 17
14 T = (Wl + WZI * (XLA + .29'll GO TO l7
15 T = lwl + W3l * IXLA + .3701 GO Tn 17
16 T = (WZ + W3l * IXLA + .4431 17 GO TO 151,52,53,541, M
C BE~RING FRICTION 3.500 PADDLE 51 IF l!,GT,1321 GO TO 55
IF (AGRP~.GT.300,1 GO TO 56 TF = 0.2 + 0,COI67 * AGRPM G'1 TO 73
5b TF = 0 0 7 GO TO 73 .
55 IF (AGRPM.GT.150.1 GO"T0-'-57 TF = 0.4 + G.0053 * 4GRPM G·J TO 73
57 TF = l.l'l G'l TO 73
1-' 1\) ~
TABLE III (Continued)
C BEARING FRICTION 3.831 PADDLE 52 IFIAGRPM.GT .400. I GO Trl 58
TF = 0.25 + 0.00237. * AGRPM GO TO 73
58 TF = 1.18 G;J Tf1 73
C BFARING FRICTION 4.000 PADDLE 53 IF IAGRP~.GT.250.I Gn T'.J 15',
TF = 0.12 + 0.0038 * AGRPM GO TO 73
154 TF = 1.01 GO TO 73
C BEARING FRICTION 4,039 PADDLE 54 IF IAGRPM.GT.240.l GO TO 5~
TF = 0,1 + 0.0041 * AG~PM GO TO 73
59 TF = 1.08 73 T = T - TF
POWER= T * AGRPM * 6.2~ I 12.0 ~p = POWER I 33000. BR= HP I IIQ I 60.l * .023571
74 PN =POWER* 3l.2 * 3600. I (DENB * AGRPM ** 3 *DA** 4*XL I CHEAT BALANCE
QAGIT =HP* 60. I ,02357 GO TO 19
18 QAGIT = O.O HP= 0.0 SR = 0. r. T = O.O PN = 0.0
19 CONTINUE DELTEC= IQ+ OAGITl I IWLBH* Cl TEOC = TEil + DELTEC TEAVGC = 114.0/22.0l*TEOC + IA.0/22.0l*TEI IF (RER.GT.1000.l Gn Tn 78 TEOL = TEOC TE/IVG = TEAVGC
ll 9 CONTl"IUE C 'FXP H NU AND J
78 DELTFC = TWM - TEAVGC DELTD = TWM - TEAVG H~ = QOA I DELTD HC = QOA * QOAR I DELTD X"IU = HC'* DI XK P~ = VISB *CI XK XJ = XNU I PR** ,333333 XJVIS = (VISWM/VISBI **a.le* XJ XJVISC = XJVIS * QOAR
C AXIAL DISPERSION PARAMhTERS BETI =HK* P * XL I (WLBH * Cl TRATIO = (TEI - TEILI I HEOL- TEILl IF HRATIO.GT.O.Cll GO TO ZO TRATIO = O.O PE= O.O PEOA = ').O
GO TU 28 20 IF (TRATIO.GT.0.75) GO TO 21
I~ ITRATIO.GT.0.251 GO TO 22 GO TO 25
21 PE= 1.5 - (2.25 + 6.0 * (TRATIO - l~Oll **0;5 GO TO 23
22 PE= .25 * 40. ** (1. - TRATIOI 23 PE= (1.0 - EXPI-PEll f TR,TIO
PE = { 1.0 - EXP(-PEI I I TR,T!O GO TO 27
25 PE= 1.0 I TPATlO 27 PcDA = 1.0 I (PE* VAT* 12.4 I (VFPM * XL l I
C OUTPIJT ZR WRIT(L,11 = TMJ
W'I.IT(L,?l = Tl·'J O•l 1 7 5 N = 1 , 1 l
l 7 5 WR IT ( l , N+ 2 l = Hd •; l WR!Ttl,14) = TEil WRIT I l, l 'i l = TE! WR!T(L,1.6) = TEO WqJT(L,17) = TEOL W" IT IL, li!) = TRATIO W~ITIL,P) = Ql Wl{!TIL,2".l) = ,, WO!T(L,21) = HC Wl{JTtl,22) = AGKPM wo l TI L, 2 3 l = RE R ~R!T(l,24) = WL8H wqIT{L,251 = TORQUE WRi T (L ,Zol = HP
C THE NtJ"!BER fJF RUNS FOR EACH AGITATOR DIAMETFR ARE 144 FOR 3.500 C FfJR ~.831 90 FOR 4.000 ANO 46 FOR 4.039
84
IF (I.EQ.144) GO TO 30l IF !1.EQ.2281 GO TIJ 301 JF (J.E0.318) GO TO 301 IF I l.E'J,3641 GO TIJ 197 G'J TO 2f:3.l
301 M =" + l GO TO 197
2Bl IF (L.LT.151 GO TO l 1Q7 WRITE (h,l9Rl 198 FOKMAT llHl ////l
WOJTf (&,20,l WRIT 201 F~R~AT (// •X
l 5X 6HTI 11 2 5X f,HT(4) 3 5X 6HTI 71 4 5X 6HH 101 5 ~X 6HTEI b 5X 6HTR.ATIO 7 5Y 6HHC ?, SX 6HWLBH q I
'199 GO TC 141 Et\JD
6HOATE 15F8.2 15FB.2 l 5Fi:l. 2 l 5F 8. 2 15F8.2 15F8.2 15F'3.2 15F~.!
l5(3X A51/ 5X 6HTY,E l514X A41 //5X 6HTl21 lSFR.2 //5X 6HT(31 //5X 6~T(5) l5F8.2 //5X oHT(6) //5X 6HTl81 l5F8.2 //5X 6HTl9l //5X 6HTll ll 15F8.2 //5X 6HTEIL //5X 6HTEIJ l5F8.2 //5X 6HTEOL //5X 6HOL l5F8.2 //5X 6HO //5X 6HAGRPM ·· l5F8.2 l/5X 6HRER //5X 6HTORQUE 15F8.l //5X 6HHP
II l5F8.2 II 15F8.2 .I/ l5F8.2 II l5F8.2 II l5FB.2 II 15f'8.2 II l';;FIJ.l II 15F8.2 II
l-' l0 00
TABLE IV
FORTRAN STATEMENTS FOR AGITATOR POWER REQUIREMENT DATA REDUCTION PROGRAM DIMENSION DAIA 141
C CURVE FIT IRON-CONSTANTAN THERMOCOUPLE TABLES IN DEG. F VS. MV TEMPCAI = 32.36685 + !35.329 + 1-.2902832 + !0011734 - •00015831
l*Al*.Al•Al*A DENCDI = 58.03 - .03413 * D VIS(El = 2.71828183 ** 111.79908 + c-.07765174 + c.0002598315 -
1 .cooooo317051 * El * El * El LPC =52 Wl = 241.5 I 453.6 W2 = 40505 I 45306 W3 • 551.0 I 45306 XL= 21.75 I 12.0 DAIA( 1) = 3.500 DAIAC21 3.831 DAIA<31 = 40000 DAIAC41 = 4.039 DAI = 305000 DA = DAI I 12.0 I • o· M = I
l READC5,1001TM1,TM2,NW,XLA,TWMV,TEIMV,TEOMV,Cl5,CIF,TIMEM,TIMES 100 FORMAT CA6, A4, 15, 8F5oOI
I = I + l TWM = TEMPITWMVI TEI • TEMP(TEIMVI TEO= TEMPCTEOMVI TEAVG =!TEI + TEO! I 2o0 DENB = DENCTEAVGI DENW = Dffl!ITWMI ViSB = ViSCTEAVGI * DENB * 2,42 I b2o4 VISW = VISCTWMI * DENW * 2o42 I 62o4 Tl = TIMEM + TIMES I 60.0 AGRP4 = 6oll * (CIF -CISJ I Tl RER = AGRPM * 60.0 * DENB * DA **2 I VISB XLA = XLA + 4o75 IF CNW.EOoll GO TO 11 IF CNW.E0.21 GO TO 12 IF CNW.EOo31 GO TO 13 IF CNWeEOel21 GO TO 14 IF INW.EQ.131 GO TO 15 IF INW.EQ.231 GO TO 16 IF CNW.EOo 1231 GO TO 116
11 T = Wl * CXLA + ell3 GO TO 17
12 T= W2 * CXLA + 0186 I GO TO 17
13 T • W3 * CXLA + 02571 C,-0 TO l 7
l', T = !Wl + W21 " (XLA + .2991 G'J T .; 17
:t 5 T = (Wl + W3J * (XLA + .3701 60 TO 17
11', T ={W2+W31 * IXLA + 0443! GO TO 17
116 T = IW! + W2 + W31 * (XLA + 0.5561 ]7 GO TO (51,52,53,54>, M
BEARING FRICTION 3.500 PADDLE ol IF !IoGT.651 GO TO 55
IF IAGRPMoGT•300ol GO TO 56 TF = Oo2 + 0,00167 * AGRPM GO TO 73
56 TF = 0, 7 GO TO 73
55 IF (AGRPMoGTel5Q.J GO TO 57 TF = Oo4 + 000053 * AGRPM GO TO 73
57 TF = 1.19 GO T) 73
C BEARING FRICTION 3e83l PADDLE 52 !FIAGRPMeGT,400.J GO TO 58
fF = 0.25 + 0000232 * AGRPM GO TO 73
58 TF = 1.18 GO TO 73
C BEARING FRICTION 4,000 PADDLE 53 IF IAGRPMeGT.250.1 GO TO 154
TF = 0.12 + 000038 * AGRPM GO TO 73
154 TF = 1.07 GO TO 73
C BEARIN~ FRICTION 4,039 PADDLE 54 IF IAGRPMeGTo240,I GO TO 59
TF = 0,1 + Oe004l * AGRPM GO TO 73
59 TF = 1.08 73 T = T - TF
POWER= T * AGRPM * 6,28 I 12.0 HP= POWER I 33000. PN =POWER* 32.2 * 3600. I IDENB * AGRPM ** 3 *DA** 4*XL ! QAGIT =HP* 60, I ,02357 IF. (l.EQ.QJ GO TO 197 IF 11,EOe 761 GO TO 301 IF lleEQ,1111 GO TO 301 IF lleEOo2l9J GO TO 301 IF ILPC,LT.261 GO TO 29 GO TO 197
30 l M = !'I + l DAI = DAIACMI DA = DAI I l2e0
1~7 WRITE (6,1981 198 FORMAT llHl llff/1
WRITE 16,1101 110 FORMAT C 4X 9HOATE 5HNW
16HTF 7H T 9HTEAVG 27HHP 8HQAGIT llHAGRPM
LPC = 0
8HXLA 9HVISW
9HRER
8HTW lOHVISB
2HPN I
29 WR!T:CC6,l201TMl ,TM2,NW,XLA,TWMtTF , T ,tEA\IGtVISWoVISB•HP,QAGITt 1 AGRPM,RER,PN
120 FORMAT llH A6,A4,14,F7,2,4F8,2,2F9,2,F9.5,F6,2,3F9o2 II LPC = LPC + l GO TO 1-END
!--" I\)
'°
TABLE V
DATA FOR HEAT TRANSF'ER TESTS WITH GULF HARMONY OIL 151 AND THE 3.500 INCH DIAMETER BLADE
DATE 03/29 03/29 03/29 03/29 03/29 03/29 03/29 03/29 03/2q 03/29 03/29 03/29 03/29 03/29 03/29 TIME 1620 1645 1710 1810 1830 1843 1900 1915 1930 1945 2005 2025 2040 2050 2060
Tl 11 124.13 121.47 122.97 119. 77 120.62 118.71 116.46 114.48 113.29 115. 68 112.98 111.27 109.83 108.94 108.33
Tl21 126.07 123.11 123.96 120.89 122.02 120.59 118. 71 117.21 116. 36 118 .40 1.16. 12 114._45 112.81 t ll.85 lll.00
Tl31 127. 02 123. 85 123.96 121. 30 122.36 121.61 118. 71 119. 32 118.78 120.59 118.92 117.31 115. 78 114.55 .113.63
Tl41 126.54 123.28 122.94 120.69 121.81 121.21 118. 71 119.80 119.60 121.23 120~25 118.88 117.48 116.22 115.30-
Tl5l 125.15 121.74 121.61 119.53 120.42 119. 77 119.26 119.19 119. 36 120.55 120. 28 119.29 118 .oo i11.01 116.12
T(61 123.17 119.94 119.87 111. 89 llA.54 ll!l .00 117.48 117. 89 118.06 119.19 119. 63 118. 75 117. 59 116.63 - 115.98
Tl71 120 .• 65 117.38 117.72 116.02 116 .19 115. 61 114.96 115. 20 115. 71 116.80 117» 72 117.21 116.36 115.47 114.92
T(81 117. 5 9 114.411 115.33 113.83 113.49 112.64 111.95 112.19 112. 9_4 113. 76 it5.03 114. 82 114. 00 113. 32 H2.98
Tl91 114.24 111._ 30 112.77 111. 37 110.65 109.35 1 OR. 46 io8.50 109.15 110. 18 111. 54 111. 54 111. 06 110.52 110.31
Tl 101 110.48 107.78 110.n 108. 84 107.61 105.55 104.49 104.18 .10,~.90 106.07 107.30 107.61 107. 34 107.10 107.13
Till! 107.57 105.04 108.29 108.53 105.18 102.95 101.21 100.79 101.20 102.47 103.36 103.84 103.81 103~67 104.05
TEil 84.78 82.02 79.94 80.11 80.91 81.60 82.12 82.50 83.43 84.40 85.57 86.06 86.33 86.68 87.13
TEI 86.96 84.06 81.33 81.02 81.99 83.16 83. 71 84. 16 _ 85.24 86.20 87.44 98.20 88.6~ 89.31. 90.10
TFO 87.62 84.37 81 •. 71 81.26 82.40 83.68 84.96 85.68 88.69 87.93 89.58 90.41 91.24 92.00 92.,;96
TEOL 87.80 85.00 82.96 83.20 84.00 84.65 R5.22 85.64 86.63 87.55 88.89 89.64 90.21 90.90 91. 73
TRATIO 0.72 0.68 0.46 0.29 0.35 o.51 0.51 0.53 0.56 0.57 0.56 0.60 0.59 0.62 0.65
OL 30.96 - 28. 79 2A.56 27.16 27.83 27.47 25.82 26.52 26.39 27.45 26. 8~ 25.93 25.04 24.23 23.65
Q 510.25 51_2.42 519. 98 519. 71 521.80 512.66 504.91 504.21 502.63 503. 28 503. 92 503.09 505.69 506.49 507.07
HC 5.44 5.81 6.09 6.14 5.84 5.84 5.70 5.68 5.4'5 5.50 5.~8 6.07 6.52 7.08 -7.95
AGRPM 101.76 100.89 59.09 5.8.60 77.79 116.50 156.73 197.37 238.28 198.39 298.47 381.28 463.67" 548.15 630.84
RER 49.7 43.8 23.3 23.1 31.9 "4·9.4 68. l 87.3 110.0 95.1 151.0 198.9 246.9 300.0 356.'7
WLBH 364.3 311. i 373~4 365.4 365.2 363.5 363.4 364.2 364.0 361.4 361.l 355.l 353.5 · .353.4 353.2
TORQUE o.o o.o o.o o.o o.o o.o o .• 0 o.o o.o o.o o.-o o.o. o.o o.o o.o I-'
HP o.oo o.oo o.oo o.oo o.oo o.oo o·.01 0.01 0.01 0.01 0.02 0.03 0.05 o.o7 0.10 \.;.)
0
TABLK V (Continued)
DATE 03/29 03/29 03/29 03/29 03/31 03/31 03/31 03/31 03/31 03/31 03/31 03/H 03/31 03/31 03/31 TIME 2110 2120 2130 2135 1110 ll20 l l'tO 1152 1202 1220 1232 1245 1257 1307' · 1314
Tl 11 108.16 104.87 101.78 103.16 120.79 120.82 124.47 122. 80 119.63 118.10 115.71 113.63 112.06 uo. 76 109.70
Tl21 ll0.52 105.76 100.93 102.33 124.88 123.28 125.g3 123.00 122.12 120.93 118. BB 116.97 ll5.47 114.24 113005
Tl3l 112. 88 106.27 99.76 l 01. 54 124.BB 124.88 126. 71 125.93 124. 19 123.17 119. 90 120.04 118. 68 117. 35 116.29
Tl4-l 114.58 106.48 99.00 100.55 125.01 125.05 126. 13 125.69 124.50 123.99 12 2. BO 121.54 120.25 119.15 118.06
Tl51 115.47 l 07 .13 98.21 9CJ.72 123.89 124.02 124.74 122.70 123.68 123.34 122. 60 121.78 120.72 119. 87 118.88
Tl6l 115.4 7 108.12 91-.66 99.38 122.29 122.29 122.87 122.53 121.98 121.95 121.61 120.96 120.28 .119.56 • 118.61
Tl71 114.45 l 08. 53 •H.32 98.49 119.77 119.73 120.59 120.04 119.53 119.56 119.43 120.93 122.15 118.13 117. 38
TIBI 112. 70 l 08. 09 97.32 97.87 116.63 116.67 117.86 118.85 116. 36 116. 39 116.60 116.53 116.;29 115.85 115.27
Tl 9) 110. 14 l 08 .64 97.84 97.90 113. ll · 112.98 114.. 75 113. 76 112. 74 112 • 64 112.88 112.91 112. 88 112.64 112.19
TC 101 107.40 105.11 98.56 98.14 126. l 7 109.15 111.51 110.18 108.46 108.33 108.29 108.46 108.46 l OB. 50 108.16
Tl 11 l 104.66 103.40 98.52 98.25 105.86 106.03 109.01 107.30 l 05.18 104.77 104.36 104.32 104.36 104.42 104.22
Ti:ll 87.99 89.27 90.99 92.16_ . 82. 29 81.84 81.77 Bl. 77 BJ.95 82.05 84.09 82.53 83.05 83.33 83.40
TEI 91.41 92.13 93.65 97.26 84.13 fl3.54 82. 78 83.16 83.65 84.06 84. 72 84. 99 85.58 85~93 86.24
TEO 94.34 96.44 99.15 101.79 85.75 !15.20 83.96 84.37 86.20 86.65 85. 86 88.00 89. 00 · .89. 79 90.17
TEOL 93.34 95.24 98.16 101.02 87. 33 86.lll! 86.'!2 86.80 86.99 87.15 89.47 88.05 88.66 89.tl 89.43
TRATIO 0.64 0.48 0.37 0.58 0.36 o.34 0.20 o. 7.8 0.34 0.39 0.12 0.45 0.45 0.45 0.47
Ql 23.20 18.26 13.91 14. 79 29.94 29.96 30.'>9 30.39 29.60 29.26 28.47 27.65 26.81 26.10 i5.40
Q 509.23 515.24 517.87 516.99 467. 91 4t>7.R9 469.22 466.84 470.31 475.41 477.86 477.02 473.10 467.01 472.44
HC 8.95 23.41 132.43 607.30 4.65 4~41 4.87 6.33 4.41 4.35 2.93 4.63 5.11 5.17 5.58
AGRPM 756.48 874.89, 986.55 10CJ3~5S 911.62 • 98.67 60.27 79.79 118.38 137.0l 176.33 215.28 255.83 296.17 337.17
RER 453.8 555. 9 687.5 857. 3 45.6 44.7 2_6.9 35.8 53.8, 63.0 87.0 102.7 125.1 147.3 169.9
WLBH . 352. 9 359. 7 359.0 358.4 200.4 200.'i 200.5 200.5 201.4 201. 4 198.4 l9t.6. -197.6 194.0 · 194.0
TORQUE o.o o.o -0. 0 o.o o.o o.o o.o o.o o .• o o.o o.o o.o' o.o o.o o.o I-'-
o.oo \.,..)
HP 0.14 0, 19 0.26 0.37 o.oo o.oo !J.00 o.oo o.oo 0.01 0.01 0.02 0.02 0.03 I-'-
TABLE V (Continued)
DATE 03/31 03/31 03/31 03/31 03/31 03131 03/31 03131 03/31 03131 03/31 03/3.1 03/31 03131 03/31 TIME 132"1 13'+0 1350 135"1 1406 1415 1643 1702 1715 1730 1745 1800. llH4 1R30 1840
T(l) 109.01 l 08. 36 107. 99 107.75 107.64 107.61 148. 8 3 162.06 156,68 164.38 167. 47 171,16 16'1, ll •149.16 lB.12
Tl21 112.23 111.61 111.13 110. 72 110.45 110.31 150. 3 8 16(,.46 159.71 168.91 172. 33 176. 18 174.2.4' 150.58. 143.-63
Tl31 115.47 114.7'1 114.21 115. 37 113. 25 113.08 151.% 170. 92 162. 53 173.77 177. 25 U!l.03 179.06 .151.46 143.73
Tl41 117. 28 116.49 116. 02 115.47 115.13 114.58 157..:>3 173.50 164.01 176.25 1 79. 59 183.34 181.40 l 52.t.4 14~'.8.3
Tl 51 118. 10 117.52 116,90 118. 17 116.15 115. 95 153. 31 174.94 165.35 177.62 180. 76 184.10 .182.33 154.15 144. 20
Tl61 117 ~9 3 117.31 116.84. 118.17 116. 19 115.!ll 155.00 174.51 165.05 177.08 1 RO. 11', 182.97 181_. 43 155,.70 145. 35.
Tl71 116.70 116.U, 115. 8 5 11 c;. 47 115.27 115.10 l 55. 84 1 72. 60 165.76 174.84 177.65 179.99 178.82 122.4"1 146.09
Tl Bl 114.75 114. 28 113.93 115.3;) 113. 39 113.29 15 5. 5 7 168.98 162.50 171.22 173.44 175.34 174.37 15'i.87 14!•.43
Tl 9) 111. 75 l ll. 41 111.10 110.93 11 o. 86 110. 72 153.99 164. 21 160.11 165.96 167.87 169. 25 168~61 154.29 146.40
TIIOI 107.92 107. 61 107.51 107.44 107.47 107. "i.1 151.!)9 158.63 156.38 159.91 l 61. 19 162.03 161.52 151.29 - 145.35
Tl l i I 104.05 103.84 104.01, 104.08 104.18 104.42 147.54 153.31 152.07 154.12 154.66 154.86 154. 79 152~94 147.98
, TEIL 83.57 83.88 84.23 84. 75 84.95 85.26 lli'>.80 115. 50 116.05 115.47 115.16 114~ 62 114.1!2 116.56 tt,r,.97
TET 86. 72 88.79 87.93 88. 38 89.03 89.48 118.86 118.28 l 18. 73 118.39 117.98 .116. 99 117.47 118. 76 ll 8.49
TEO 90.55 91.10 91.82 92.44 92.99 93.51 123.94 122.24 123.16 120.09 121. 62 120.36 120.87 123.77 124.11
TEOL 89.84 90.32 91.00 91.80 92. l 9 92.74 121.94 12 2. 26 122.99 122.09 121.n 121.0!l 121. 33 123-.44 124.0fo
TRATIO 0.50 0.76 0.55 0.51 0.56 0.56 0.29 0,41 0.39 0.44 0.43 o. 37. 0,41 0.32 0.21
Ql 24.90 24.41 24.10 23.76 23.55 23.20 49.30 66.67 58. 78 69.0? 71.92 75. 21 73.50 49.77 43.13_
Q 475.00 471. 79 473. 74 4 74. 09 474. 30 474.64 1318.95 1306.03 1307.78 1282.54 1279.65 1267.~3 1275.33 1294.00 1298.96.
HC 5.95 6.36 6.61 "1.73 7.20 7 .-so 23.89 10.58 14.16 9.84 9.26 8.25 8.73 21.M, 32.46
AGRPM 378 .14 414.99 462.21 503.69 547.85 569.75 348.06 305.02 318.38 2M,. ll 225.55 185.00 203.79 34 7. 21 387;.56
HP 193.9 222.1 248.6 278.3 308.5 339.0 585.0 492.6 .'57.4. 'I 42fl. fl 359. l 287.4 320.0 577. l 650 .• ::l
WLBH 194.8 194. 7 193.8 193. 7 197.l 19A.O 391. 8 395.8 395.6 395.8 397. 7 399.7 399. 7·- 399.l 395.3
T(IRQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o I->
HP 0.04 0.04 0.05 0.06 0.07 0.08 J.Ol o.oo 0.01 o.oo o.oo o.oo o.oo 0.01 0.02 \.,.) l\)
TABLE V (Continued)
DATE 03/31 03/31 03/31 03/31 03/31 03/31 03/31 03/31 03/31 03/31 03/31 03/31 04/03 04/03 04/03 TfME 1851 1904 1914 1925 1936 1950 2000 2010 ?020 2030 2040 2050 1500 1515 1545
T( 11 135.27 135.84 133.64 132.86 134.01 133.84 133.03 133.16 132.89 133.03 133.54 133.98 168.54 168.14 172. 73
Tl 21 133.54 134,05 132.15 131.50 133.50 133.67 132.82 132.86 132.96 133. 20 133.67 134.21 168.04 i,65.45 169.45
Tl 31 131.77 132.25 130.52 129.91 132. i?l 132.62 132.32 132.25 132.35 132. 72 133.23 133. 71 166. 13 162.94 . 166.80
Tl41 130.79 131. 30 129. 74 129.12 131. 30 131.81 131.37 131.47 131.77 132. 15 132.65 133.20 165.62 162.60 · 166.39
Tl51 130.08 130,65 129.33 128.48 130,48 130.92 130.41 130. 79 130.99 131.47 131.94 132.52 163.91 161.69 Hft.75
Tl61 129.7ft 130.41 129.84 128.21 129.91 130.14 129.80 130. 01 130.28 130. 79 131.26 132. 01 162.87 163.37 164.88
Tl 71 129.60 130. 55 132.0l 128.75 129.23 129~43 129.16 129.50 129.74 130.11 130. 75 131.33 162.43 165.2:> 165.59
TIBI 130.14 131.57 134.21 129.91 129.50 129,06 128.75 129,09 129.57 129.57 130.0l 130.96 H,2. 94 169. 7Z H,8, 7!!
Tl 91 1'12.18 134.05 136. 3 8 132.38 130. 72 129.60 129.12 129.26 129.06 129.26 129. 60 130.38 165.35 1 r~.f-'• 175.04
Tl 10 I 134.42 136.38 137.57 134.08 130.55 130.31 129.60 128.95 128. 92 128.99 129.26 130.01 167.33 176,68 176.99
Tl 111 134.52 135,91 136,R6 133. 71 131.47 129,74 128,75 128,61 ll7,97 128,ll 128.41 129.09 165.25 1 74. 57 177, 45
TEil i 17. 65 117.~!! 117. 35 117 .42 117,93 117.72 117.14 117.55 117. 72 118,10 118.61 119. 36 137, 13 136.76 138. ll
TEI 118 .66 ll8.59 118,73 it9.17 119. 72 119.51 119.'.)0 119.44 120.02 120.70 121.25 122. 24 138. 20 137.32 BB.bl
TEO 124. 65 124.45 124.48 124.99 125.30 125.34 124.96 125.27 125. 8 l 126.46 127, 14 127.89 146.52 146.12 147.06
TEOL 124. 9'5 124.64 124.75 124.99 125.58 125.0l 124.54 124.74 125.18 125.69 126.20 127.12 146. 02 145.76 l47.3R
TRATJO 0.14 0.17 0.19 0.23 0.23 0.25 0.25 ·0.26 0.31 0.34 o. 35 0.37 0.12 o.oe, 0.05
QL 33.84 34.19 33.12 32. 71 34.19 34.55 34.24 34. 31 34.52 34.78 35.13 35.'il 60. 09 57.63 60.73
Q 1314.34 1304 .• 52 1302.88 1312.76 1311.27 1306.51 1309.53 1319.98 1298.77 1316.78 1319.81 1317.74 2668.29 2704.68 2714.24
HC 90.97 82.54 103,99 118.18 93.19 81.37 82. 79 82.45 82.88 85.77 86~30 91.07 63.25 76.08 66.86
AGRPM 429.64 409.39 470.79 514 • .37 556,39 597.22 638.66 682.30 763.10 808.91 850.22 893.27 309. 5.6 267.22 226.83
RER 735.0 695.6 802. B 885.6 975.1 1032.7 10137.8 1112. 7 1331.6 1436.6 1534.2 H,5B.6 952.2 Blli.4 1l6.5
WLBH 395.1 391.6 391.6 391.5 391.4 391.5 3'H. 6 391.6 393. 2 393. l 394.8 394.6 609.6 6H.5 594.6
TORQUF. o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o. o.o o.o o.o o.o I->
HP 0.02 0.02 0.03 0.04 0.05 0.05 0.06 0.01 Do lO 0@ 1 l 0.13 -0.14. o.oo o.oo o.oo \.).) \.,.)
TABLE V (Continued)
DATE 04/03 04/03 04/03 04/03 04/03 04/03 04/03 04/03 04/03 04/03 .04/03 04/03 04/03 04/03 04/03 TIME 1600 1610 1622 1640 1653 t705 1715 1730 1739 1750 1803 i813 1822 1830 1840
Tl 11 1 71.49 169. 92 16q,9g 168.41 167.10 166.43 165.52 165.42 164.25 163 .91 162. 90 161.76 161.02 161.22 161.83
TI 21 168.74 169. 5 ii 168.61 168. 14 167.2'.) 166.73 165 .• 82 165.76 164. 61 164.41 163. 64 162.50 161. 42 161.76 162.30
Tl 3 l 167. 70 167.47 166.86 167.30 166.02 165.76 165.3.5 165.08 164.18 164.18 163.20 162.23 161.29- 161.49 162.10
Tl 41 166. 73 166. 02 lbt',.02 166.53 H,5.45 164.98 164.51 164.38 163.71 163.61 162. 60 161.76 160. 82 161.09 161.52
Tl 51 165. 79 163.54 164.72 164.78 164.08 163.64 163.10 163.24 162.36 162.33 161.52 160.65 159.78 159.98 160.35
T(6l •t 67 .40 163.37 164.ll 163.78 163.24 162.77 162.30 162.20 161.56 161.66 162.53 159.84 159.04 159.24 159.54
Tl71 169.38 l 62. 73 163. 27 1 63. 00 162.53 162.26 161.52 161.52 160.72 160.68 159.67 158.87 158.06 158.33 158.70
Tl 81 l 73. 60 164.72 162.70. 162.90 U,2.23 161.62 160.89 160.65 159.88 159.91 158.83 157.w, 157.19 157.49 157.86
T(91 178.25 168.47 164.35 163.34 162.67 161.52 160.41 159.98 159.17 159.04 157.99 157.29 156. 71 156.71 1.57.15
TI 10) 1 F!O. 63 170.55 l 65. 0 8 164,82 162.73 160.68 160. l 5 159. 81 158.70 158.40 157.45 156.51 156. ll 1%.14 l'H,.61
Tl l ll 178.42 169. 41 163.61 162 .50 160.58 158.87 157.96 157.52 156.48 156.14 155.13 154.36 154.19 154.19 154.42
TE!L L:H.94 U8. 38 138. 42 138. 55 138.55 13'!.89 138.79 139. 13 139.53 140. 18 139. 77 139.36 138. 96 13fl.76 138.31
TEI · os.57 139. 35 139.96 140.10 140.44 140.64 140.81 141.28 ·, 141.89 142.97 142.84 142.77 143.0l 142.60 141,48
TEO 147.84 147.84 147 0 74 147. 70 147.97 149.24 148. 58 148.89 149.49. 150.30 149.96 149.83 149.73 149.43 148065
TEOL 147. 20 147.44 l 46.97 146. 90 147.24 147.68 147.78 148.22 1411.59 149.40 149.23 149.03 149. 03 148. 73 llt8. 05
TR A TIO 0.01 0. 11 0.18 0.1'1 0.22 0.20 0.22 0.24 0.26 0.30 0.32 0.35 0.40 0.39 0.33
OL 61.00 60.42 60.42 ~0.84 5'l. 91, 59.57 59.19 59.08 58.53 58.4'5 57.63 56.96 56. 20 56.42 56.77
Q 2713.97 2703.39 2710.62 2728.33 2738.91 2749.61 2769.15 2783.57 2789.02 2A04.4l 2800.31 2790.60 2791.35 2795.10 2793.24
HC 67.87 11. 58 67.62 66.33 70.61 74.20 77.53 79.12 85.05 91.33 99.95 99. 4l. 106. 97 lD2.'53 94.40
4GRPM 245.94 286. 70 329.08 348.42 389. 3'l 433.37 4U,.8B 519.06 596. 04 M4.l0 112.n B%.o9 948.55 907.71 1'71.64
RER 774.4 913.2 l 046. 0 1107. 7 1748.C) 1402.R 1%8. 7 1705.6 1904.6 2]28.7 2619.ll l89l.O 32Hl.4 :)04':i.5 25He4
WLBH 594.6 605. 6 605.8 606.T 606.5 6(ll. 2 601.2 601.0 600.8 604.8 604 .• 9 599.8 '599.8 Ml.5 Ml2.8
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o. () o.o o.o I-'
HP o.oo o.oo o.oo 0.0() o.oo o.oa 0.02 0.02 o.o,;, CT. O"i 0.01 o. to O.B o<Y i 11 0.07 w ~
TABLE V (Gont:i.nued)
DATE 04121 04/21 04/21 04/21 04/21 04/21 04/21 04/21 04/21 04/21 04/21 04/21 04/21 04/21 04/21 TIME 1053 1105 ll.20 1136 1156 1715 1238 1255 1310 J 332 1355 1410 1420 1432 1450
Tl 11 149.94 148. 59 145.99 149.94 153. 31 157.69 l 63. 5 7 171.09 175.58 153.14 145.38 145.35 143.49 141.12 136.38
T(21 153.55 153.95 151.09 155,54 I 59. l7 H,3.61 169.45 176.48 180.63 158.93 150. 38 150.38 148.25 145.35 140.01
Tl 31 160.72 159 .41 156. 38 161,19 165.05 169.75 l 75. 2 8 181,66 l84.f!4 164,75 155,87 155~ 70 153.48 150.21 144.34
T( 4) 162. 06 160.82 l 57. 8 2 162.57 166.23 170.96 176,31 181.93 184.60 165,92 157.29 157.05 153.25 151,66 14-6.03
Tl 51 165,22 163,91 160.95 165.69 169.31 173,80 178 .66 182,77 184,17 169.55 160.41 160.21 158.03 154,79 149.20
Tl 61 163. 74 162 ,5 7 159. 74 164.35 167.57 111. 83 175, 98 178. 62 179, 29 167.67 159.37 159. 17 157,49 154.15 149.27
Tl71 163.00 161. 86 159,00 163034 166.56 170.35 173.94 175.68 175. 71! 166.43 158,70 158.40 156.34 153,31 148. 63
Tl 81 159.37 158.26 155. 54 159.57 162.50 165.69 168. 6 l . 169. 5.8 169. 21 162 .33 155.23 154.93 153.01 150.21 145.99
Tl 9) 154.12 152. 94 150.41 154,09 156.65 159 .37 161. 73 161..86 161.52 l 56. 5 5 150.28 149.87 148. 19 145.65 141.97
T! 101 147.04 146.03 143.69 146. 73 148.83 151.12 152.94 152.98 i 52. 64 1411.86 143.66 143.29 l4l., 87 139.84 H7.03
Tl 11 l 139.64 138.55 136, 72 1 38. 92 140.68 142.54 144.30 144.Bl 1,,5.35 140.112 136. R9 136,52 135. -,,7 134.11 131. 94
TE IL 95.12 94.43 94,09 93.64 93.19 92.68 91.99 91,68 91.16 93. 71 94.67 94,40 94.23 94.60 95.02
TEI 101, ll 100.32 100.49 98,91 98.26 97.50 96.54 94.89 95.16 'Hl.67 101.21 100.83 101.00 101.76 1:)2. 38
TEO 108.89 107. 96 107.93 106.53 10 5. 70 104.64 103.27 101.42 99.73 106. 22 108. 58 108 .14 108.41 109.09 Hl9. 71
TEOL 107. 72 107,26 107.21 10.6.27 105.87 105,15 104.32 l.03,84 103.19 105.80 HH.33 107.02 UH. l.3 107.111' rns.53
TRATIO 0,48 0.46 0.49 0.42 0.40 0.39 0.37 0.26 0.33 0.4ll o. 52 o •. 51 o.53 0.54 0.54
Ql 57,20 56,20 53.82 57.61 60. 59 64.52 69-.08 73.97 76.34 60.34 53.39 53.21 50.24 49.02 44.76
Q 1312.75 1335.04 1328.46 1315.75 1329.59 1312.23 1307.68 1299.38 1294~26 1294.60 1309037 1305.ll 1318.66 1326.03 1321.38
HC 9,87 10.24 IO.BO 9.60 8.98 8.03 1.10 6,23 5.92 8.64 l.0,94 R0.92 n.:n 12.132 15.13
AGRPM 302,18 301.88 341.72 261.56 220.90 .. 180.34 139.'n 101.08 01.79 220.58 344.27 344.23 385.00 467.48 553.46
RER 290.9 284.7 322.6 236,8 196.4 156.2 117. 3 02.0 65.6 196.<? 329.0 325.0 365.3 45'5.o3 551.5
WLBH 216.6 2H,. 7 216.7 216,8 217.<? 218.0 219. 2 220.4 221.6 zn.-. 222.2 222.2 222.2 2:22. l 224.3
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o . o.o o.o o.o o.o o.o f--'
HP o.oo o.oo 0.01 o.oo o. ()() o.oo 0$00 o.oo o.oo o.oo o.oz 0.02 0.02 0(1)03 0.05 \.;.) Vt
TABLE V (Continued)
DATE 04/21 04121 04121 04/21 04/21 04/21 04/21 05/24 05124 05/24. 05/24 05/24 05/Vt 05/24 05/24 TIME 1510 1528 1540 1550 1600 1610 1620 1147 1355 1430 1460 1525 1550 1625 165.0
T{ll 126.17 123.04 121.27 122. 19 123.21 124.16 124.74 123.82 147.68 143.32 138. 86. 134. 8.3 131.98 129.91 i28.72
T(21 126. 71 123.17 120. 25 121. 71 123.04 124.16 124.57 127.43 149.30 145.55 141.77 138.15 135.57 133.60 .. 132.62
Tl31 127.22 122.80 118. 23 120.55 122.12 123.17 123 .96 131.13 150. 21 147.34 144.30 141.33 139.13. 137.23 136.38 ..
Tl41 128.24 122. 42 116.73 119.43 121.27. 122.42 123.21 133.03 149.84 147.24 144.84 142.61 140.95 139.06 138.45.
TIS) 129.84 121.95 114.41 117.72 119.56 120.89 121.'H 134.52 148.59 146.26 144.44 142.61 141. 29 139.94 139.43
Tl61 · 132.04 122.05 113.. 39 115.54 118.00 119. 63 120.59 134.52 147.04 144.37 142 •. 75 141.33 140.48 139.43· 139.09
Tl71 132.96 122.83 113.83 113. 76 116. 36 118.13 119.09 133.40 144.64 141.50 139 .• 94 138.82 138. 31 137.57 137.57
T(8.J 132 .1!6 124.40 115.78 112.64 114. 79 116.5 3 117. 76 131.13 141.67 138. 11 136~45 135.44 135.23 134.83 134.86
Tl 91 131.70 124.84 117.69 113 •. 46 114.00 · U5.85 lH,.87 i27 •. 80 138. 42 134.15 132.15 131.16 131. 13 130.89 l;H .13
Tl 101 129.29 123.99 119.26 114.92 114.00 115.44 116.73 123.45 134. 86 129.84 127.39 126 .• 27 126. 20 126.00 126.27
Tllll 125.93 121.85 118.57 114.75 113. 59 114.58 115.47 118. 85 131.81 .126.44 123.41 121.95 121.61 121.44 119 .• 90
TEJL 95.81 96.63 97.56 98.18 99.07 99.90 100.45 87.99 86.;09 86.51 86. 71 87.13 87. 71 88.34· 88.58
TEI 101.52 102.14 103.13 103.92 105. 70 107.18 108.31 95.23 87.31 88.82 89.76 91.13 92 •. 24 93.41. 94.47
TEO 111.25 112.34 11.4.12 115. 76 117.12 118. 32 119.24 104.16 90.93 93. 51 96.75 100.04 101. 59 102.58 103.;48 ·
TEOL 110 .20 111. 98 113.79 114.24 115.71 ll 7 .07 117.96 103.03 99.35 99.61 100.02 100.66 101.57 102065 102.97
TRATrO 0.40 0.36 0.34 0.36 0.40 0.42 0.45 0.48 0.09 0.18 0.23 0.30 o .• 33 0.3.~ 0.41
OL 32.ll 28.23 24.56 26.28 27.47 28.23 28.74 35.39 47.63 45.67 43.88 42.24 41.03 39.66 39.22
0 1338.49 1354.05 1357.72 1357.71 1354.81 1351.29 1367.63 510.98 478.85 477.43 479.22 481. 9i 482.07 489.36 497.05
HC 33.63 52 .31. 127.76 82.28 81.10 83.41 84.89 5.78 3.11 3.54 3.42 3.39 3.52 4.14 · 4~.30
AGRPM 639.79 716. 30 806.2.9 890.00 962.71 1005.62 1034.13 209.61 21.48 40.71 59.52 79.80 98.70 Uil.71 138.71
RER .654.6 768.3 911.0 1025. 6 ll70.3 1281.3 1360.8 167.7 14.1 27.5 41.l 57. R n.2 .9i..8 l-09'.i
WLBH 224. l 222.7 222.4 221.2 221.0 220.R 220. 7 75.4 · .7.6.2 11.0 76.2 75.4 73.7 12.·4 73.1
TORQUE o.o o~o o.o ·o.o. o.o o.o o.o o.o o.o o.o o.o o.o .o.o o .• ·o o.Q I-'
HP 0.07 0.10 o.n 0.11 0.21 0.22 o •. 24 0.01 o.oo o .. ocr OoOO o.oo o.oo \.;.) OeOO o.oo a--
TABLE V (Continued)
DATE 05/24 05/24 05/24 05/24 05/24 05124 05/24 05/24 05/24 05/24 05/24 05/24 05124 05/24 05/30 TIME 1720 1750 1820 1850 1915 1940 2000 2025 2045 2110 213'5 2200 2225 2255 1506
Tl l I 126.20 124.36 123.24 122.49 120.21 119.29 115.85 114. 79 114.14 115.61 117. 38 119.05 121.61 124.88 1'14.47
Tl21 129.97 127.94 126. 51 125.45 122.77 121.47 116.05 114.00 113.35 114. 79 116.97 118.88 121. 51 125.0l 191.11
Tl31 133.74 131.57 129.94· 128. 55 125.76 124.09 118. 03 112.53 111.92 113.25 115.91 118.37 121. 16 124.67 197.94
T(41 135.88 133.67 132.04 130.41 127.39 125.62 121.40 110.82 110.79 111.37 114.41 117.42 120.55 124.19 201.00
tl51 137.06 134.93 133.30 131.50 128.41 126. 54 123. 31 109. 32 110.65 109.70 112.09 115. 98 119.53 123.72 203.95
Tl61 l 37 .06 134.93 133~43 131. 77 128.55 126.68 124.02 108.46 111.85 108.64 110.04 114. 31 118.47 122.80 203.95
Tt71 135.67 133.81 132.32 130.82 127.60 125.79 123.55 108. 12 113. 42 107.78 108.46 112.06 117 .07 121. 78 2.01. 66
T( 81 133. 37 131.67 130.31 129.09 125.86 124.19 122 .22 108. 77 114. 34 107. 27 101.44 109.80 11,; .·1a 120.79 l'l7.07
Tl91 129.84 128.31 127.26 126.34 123.28 121.81 _120. 21 110.00 114. 41 107.75 l 07 .06 108.09 114.58 119.77 1 qo. 34-
. Tl 101 125.32 124.09 123.21 122.70 120. ll 118.92 117 ._76 110. 52 H3.97 108.50 107.44 107. 71 113.113 llA.92 l-iH.26
Tl 111 120. 72 119.63" 118.95 118.92 116. 80 116.02 115.23 110.00 112.80 108 .43 107.68 107.64 113. 05 llA.06 171.42
TEil 88.92 89.20 89.61 90.58 90.64 90.95 91.02 91.26 91.13 92.02 92.47 92.92 93.85 95.05 103.81
TEI 95.3.7 9_6.44 97.40 99 • .!9 99.70 100.56 101~21 102.03 101. 86 102.55 103.58 104.81 uo.10 116. 37 112. 65
TEO 104.81 105.22 106. 01 107.25 108. 55 109.47 110.80 116.03 Hl.52 113.98 115. 52 117 .. 36 120."36 124008 124.96
TEOL 103.52 104.51 105.28 106.82 107.53 108.97 110.07 112.22 lU.29 H3.73 l.15.43 116.36 119. 36 123. 00 123.97
TRATIO 0.44 0.47 o.5o 0.54 0.54 o.n 0.53 0.51 0.53 0.48 0.48 0.51 0.66 0.1& 0.44
Ql 37.39 . 35.F.14 34. 71 33.59 31.53 .30. 34 27.56 20.88 20.86 21.21 23.10 24.99 21.01 29.39 91.47
Q 501.67 503.22 505.42 503.76 503.03 503.15 510.85 517.54 516.49 518.92 519.18 518.36 '516.34 510.09 1934.19
HC 5.02 5.57 6.23 7.50 8.133 10.-36 10.67 193.15 124.22 345.90 116.92 . 53. 37 65.67 73.81 JO.TT
AGR.PM 178.-52 218 .10 • 256. 08 340.12 422. 96 ' 508. 75 594.46 676.08 635.93 719.93 761. 39 839.97 970. 38 2958. 2(, 2cn. 75- ·
RER 144. 7 183.5 222.1 313.3 398.l 500.l (i04. l 728.0 669.4. 806. 5 896.3 1024. 2 1352. 8 4744.', .317.6
WLBH 72.9 73.0 72. 7 72.6 "74. 3 74.6 76.7 78.4 77.3 79.9 79.5 82.3 83.9 86.2 193.2
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o OoO o.o o.o o.o o.o o.o ..... \>.)
HP o.oo 0.01 0.01 0.02 0.03 0.05 0.07 o. rn O.O!l o.n o.n 0.17 0.22 o.,,,. o.oo --..J
TABLE V (Continued)
DATE 05/30 05/30 05/30 1)5/30 05/30 05/30 05/30 05/30 05/30 05/30 05/30 05/30 06/01 06/01 06/01 TIME 1540 160(, 1630 1700 1730 l!.100 1835 1006 2007 2(145 2117 2150 1625 1700 1730
Till 179.26 175.98 l 12.10 149.43 156.31 145.55 151.46 146.43 145.99 145.72 145. 65 146.16 158.73 166.29 182.30
T(21 185.14 181.66 177.32 150.24 156.81 143. 19 151.80 145.55 145.55 145.69 145.65 146.26 164.25 1.72.60 188.54
Tl31 191.98 187.97 183.07 151.22 156,78 139.94 150.75 143.36 ·144.07 144.54 144.88 145.69 169.92 178.66 194. 57
T(4l 194. 81 190.74 185.67 154, 12 158.80 141.29 151.73 141.33 142.78 143.56 143.<J6 145.01 172,93 181.93 197.10
Tl5l l<J7.67 l g3. 51 188.34 158.16 163.88 144.54 152.64 136.66 13<J.77 141.16 142. 10 143.46 175.41 183.94 1.97.80
Tl6l 197.80 193. 67 188, 5 8 161.12 167.80 144.03 154. 29 133.98 137.03 13<J. 23 140.28 142,00 175.64 183.77 .196.0l
Tl7) 195,81 191.78 186,91 163,07 169.88 14'l.60 156.ll 132.15 134. 21 136. 93 138.28 140.24 17'3.94 Hll.66 192.14
Tl8l 191. 61 187. 74 183.17 163.84 169.98 150.99 157.6<J 131. 37 132.38 134. 5 5 136, 35 13B.5<J 170,42 177,52 186.17
Tl 9) 185.34 181.87 l 77. 89 162. 30 167.57 151.29 157, 35 l38.8<J 133. 27 132.86 134. 62 136.'l'l 165.32 l 11. 5g 178.49
T 110 I l 77 .02 l 74.17 l 70. 99 158.80 162. 87 150, 3.8 153.18 139. 43 134,89 132.82 133.60 135, 84 158. 46 163.67 169.01
Tl 111 167.<JO 165.89 163.57. 153.65 156.85 146.94 150.24 137.57 134.42 131.16 lll.50 133. 64 150.89 155.17 15'l,74
. TEIL 103.98 l 04 .18 104,3<J 106.07 10.5.93 107.47 107. 10 11)8, 74 1 00. 67 lO<J.87 109.70 110.69 102.64 102.16 l:Jl,34
TEI 113,23 113,78 114.63 113.23 113.115 113.23 113.03 113. 7l 114,63 116.65 118. 66 .122. 97. 108,92 107,<J3 105.36
TEO 124,99 125,40 126.12 12 B. 06 127.38 129.38 129. 5 2 131. 45 132.06 l3l.59 134.03 135.69 117.67 116,13 114. 36
TEOL 124.28 124. 73 125.18 128.56 128.72 130. 85 129,lll 133.00 131.26 132. 69 132. 86 134.55 116,94 115.64 114.28
TRATIO 0,46 0.47 0.49 0,32 o.35 0.25 0,26 0,20 0.26 0.30 o.3g 0.51 0.44 0.43 0.31
QL 85.64 81.89 77.29 50,92 54.5') 41.27 49,07 41.30 42.36 47..9"1 43.23 44,01 66.19 73.97 87.79
Q 1928.42 1932.18 1942.95 2014.38 2033.42 2042.55 2023.00 2050.12 2049.83 2045.0R 2052.38 2028.06 1360.75 1339.37 132W.35
HC 11,85 12.69 14.0l 31.62 29.65 53.64 37.78 79.99 62.AS 66,21 67. 25 73.61 10.01 8.08 &.10
AGRPM 242,99 283,29 344.62 406,26 377.07 445.47 405.'!8 508.36 592.41 676.13 765, 10 892'.33 260.00 179.71 99.35
RER 3A5.6 4,;6.5 565.8 701,9 657.9 804,7 716.9 962.2 1095.B 1314. 0 1524,7 1921.2 337.3 224.l 116 •. 6
WLBH 194. l 193. l 194.0 191. 0 168.4 189.0 190.0 185.5 184.<J 186.3 Hl7,9 188.6 198.6 203.4 208.5
TORQUE o.o o.o o.o o.o .o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o j--' 1u)
HP 0,01 0.01 0.02 0.03 0.02 0.03 0.02 0.04 0.06 0.08 o.n 0.16 0.01 o.oo . o.oo 00
TABLE V (Continued)
DATE 06/01 06/01 06/01 06/01 06/01 06/01 06/01 06/01 06101 05/30 05/30 05/30 06/01 06/01 06/01 TIME 1800 1830 1852 1921 1943 2011 2030 2045 2136 2-045 2117 2150 1625 1700 1730
T( 11 1 72. 97 155.40 140. 62 1 32. 62 133.13 134.42 136.38 138. 38 134. 62 145.72 145.65 146.16 158.73 166. 29 182.30
T(21 179.29 160.04 140.79 131. 87 133.03 134.49 136.52 138.62 134. 38 145.69 145. 65 146.26 164.25 172.60 188~54
Tl31 185.47 165.08 140.08 130. 14 132.18 134.05 136.21 138.38 132. 72 144.54 144.88 145.69 169.92 178.66 194.57
Tl4l l 88.44 167.94 140.79 128.07 131.26 133. 37 135.74 137 .91 l 30. 99 143.56 143. 96 145.01 172.93 lBl.93 - 197~10
Tl 51 190. 0 l 169.95 141.70 121.47 129. 46 132.01 134.69 137.03 127. 77 141.16 142. 10 143.46 175.41 183.94 197.80
T(61 189.44 170.25 142.98 123.17 128.04 130.92 133. 71 136. 08 125.45 139. 23 140.28 142.00 175.64 183.77 · 196.0l
Tf71 186.64 168.76 144.34 122.19 126.34 129.46 132.55 135.10 124.57 136.93 138.28 140.24 173. 94 181.66 192.14
Tl81 182.00 165.69 144.71 121.88 124.64 128. 11 131. 26 133.98 126.27 134. 55 136. 35 138.59 170. 42 177.52 186.17
T(9l 1 75.38 161.32 143.86 124.64 123.34 126.88 130.26 132.96 128.41 132 • 86 134.62 136.99 165.32 171. 59 178 .49
Tl 10 l 166. 76 155.47 141.33 126.17 122.97 126.10 129.43 132.15 - 1290 74 1132.82 133.60 135.84 158.46 163.67 169.01
Tl 111 157.93 149.13 137.64 125. 59 122. 46 124.54 127.87 130.62 128. 6l 131.16 131. 50 133.64 150.89 155.17 159. 74
TEIL i02.64 104~32 105.52 106.27 107.54 108.46 109.32 110.93 106,89 109.87 i.09.70 no. 69 102.64 102.16 101.34
TEI 107.69 111.10 110.15 i10.02 112.58 116.82 121.49 124.69 l ll.. 04 lH,.65 l.18. 66 122.92 108.92 107.93 105.36
TEO 116 .10 119.65 121.39 123.09 125.34 127.6!! 130.67 133.25 124.65 133.59 134.03 135.69 117.67 116.13 114.36
TEOL 115.83 119.00 121.16 123.01 124.36 126.68 129.63 132.04 124.62 132. 69 132. 86 134.55 116.94 115.64 114.28
TRATIO 0.38 0.47 o. 30 0.22 0.30 0.46 o. 60 o.65 0.23 0.30 0.39 0.51 0.44 0.43 0.31
Ql 79. 79 62.00 40.91 31.99 34.17 35.63 37.29 36.84 33.98 42.93 43.23 44.01 66.19 73.97 87.79
Q 1315.51 1349.61 1372.43 1359.25 1379.17 1366.96 1374.32 1380.76 1385.61 2045.08 2052.38 2028.06 1360.75 1339.37 1328.35
HC 7.21 11.46 30.48 130. 73 67. 79 72.38 81. 3l 86.34 71.95 66,21 67.25 73.61 10. 01 8.os 6.10
AGRPM 138.30 340.12 465.60 596. 19 759.89 934.76 1090.14 1055.97 '594.68 676.13 76'5. 10 892.33 260.00 179. 71 99.35
RER 172.7 473.3 669.2 888.7 1199. 2 1620.4 2107.0 2211.0 '926.6 1314. 0 1524.7 1921..2 337.3 224. l 116.6
WLBH 203.4 194. 7 194.5 190.B 192. 3 190.3 1'35.l_ 184. 8 l82o5 l!lbo 3 HH.~ 108.6 198.6 203.4 208.5
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o 0.-0 o.o o.o o.o o.o o.o I-'
0.03 o. 06 0.10 0.17 0.25 0.26 0.06 o.os o.u -Q. 16 o. 01 o.oo o.oo -Iv.) HP o.oo 0.02 '°
TABLE VI
DATA.FOR HEAT TRANSFER TESTS WITH GULF HARMONY OIL 151 AND THE 3.831 INCH DIAMETER BLADE
DATE 04/23 04/23 04/23 04/23 04/23 04/23 Oft/23 04/23 04/23 04/23' 04/23. 04/23 · 04/23 04/26 04/26 TIME 1455 1510 1527 1542 1552 1610 1625 1640 1708 1735 1805 1832 1815 1135 1148
TUI 143.36 142.98 144.34 145.69 14·8.05 147.95 151.80 158.13 159~20 158.90 158.16 169.75 146.40 140.28 142.54 ·. Tf2l 148.15 147.54 147.17 152.57 153. ::n 153.28 157.05 162.83 164.01 163.57 162.94 173.67. 151.53 145.99 148.39
H31 153.65 152.91 154. 69 156. 61 158.97 158.97 162.63 167.54 168.64 168.31 167.67 177.18 i57~35 ,152.10 153.01
Tl41 157.25 156.65 158.33 159.57 161.42 161.29 164.25 168.44 169.61 169.21 168.41 177 ~ 18 .15'9. 30 156.18 158.63
Tf 51 159.37 158.90 160.2 5 161. 73 163.61 163.44 166.23 169.58 170.72 170.25 169 .• 5'5 176.75 162.53 158.16 -160.38
TC6J f57. 82 · 157 .52 158.36 159.41 160.85 160.58 163.00 165.79 166.86 166.46 165.72 112.10 · 160. 85 157.96 159.84·
Tl7) 157 .59 157.29 158. 23 159.37 160.85 160.72 162.70 165.12 166.13 165.62 165. 08 170 .• 59 160.31 156.28 158003
HSI 153.85 l53.58 154.53 155. 60 156.95 156.81 158.56. 160.75 161.69 161.22 . 160.65 165.69 156.61 152.30 154.02
TC9l 148.42 148.12 149.06 150.04 151.46 151.29 152. 81 154~ 86 ·155. 77 155.30 154.66 159.67 1.51.09. 146.57 · 148. 19
THOI 141.73 141.53 142.27 143.02 144.23 144.l3 .145.48 147.68 · 155.11 148.05 147.."41 152. 77 144.07 139~50 140.79
T( 11) 135.33 135.33 135.57 136.21 137.33 137.23 138.52 141.19 141 .. 94> 141..50 140.79 lF.OO 137.37 132.35 U3.54
TEIL 97.84 97.87 •H.05 '96.32 95.64 95'.46 94. 7-S 94.19 95. 05' 93.88 94.05 94.09 96.98 ·. 92.64 .92.37
TEI 102.89 103.44 102.24. 101.11 100.04 99.84 98.81 98.02 ,, 98. 77 97.85 97.54 97.50 101. 76 97-. 50 97.05
TEO 108.89 '109.57 107.52 106. 35 105.67 1Cl5. 53 104.50' 102. 62 103.41 102.58 102.14 99.84 107.07 102.50 102.00
TEOL 109.90 110·.11 108.77 107.91 107.06 1.01.02 106.27 105.64 106.26 105.27 105.39 105.35 108.84 103.66 103.23
TRATIO 0.42 Oo46 0.44 0.41 0.39 0.38 0.35 0.33. 0.33 o.35 o. 31' 0.30 o.r.o o.r.4 0.43
QL 53.37 52.89 54.22 55~21 56 .• 69 '56.58 58.97 62.42 63.40 63.06 62.39 69 .• 83 54.99 52052 54.46 '-'
Q 1329.97 1370.96 1327.41 1321.96 1320.48 1320.58 1322.66 1320.92 1308.26 1321.98 1322.65 1319.70 1331.76 i3ts.85 1322.1)4
HC 9.76 10.38 9.12 8.85 8.45 8.48 a.19 1.n 7.48 7.60 7. 76 6.86 10.16 9.41 7.7,8
AGRPM 298.88 123.71 258.68 217.59 179.28 178.86 139.95 100.44 100.55 100.22 99.84 61.32 217. 59 '2-57. 70 2u:..90
RER 370. 3 155.1 309.9 252.0 200.9 199.7 151.6 106.1 - 108.8 tor.. 7 104.2 63.9 259.5 258.3. 213 •. 9
Wl8H 237.6 237.6 241.7 241.8 240.6 240.6 239.·4 239.5 242. l 240.9 242.2 242 •. 2 237 .. 7 258.3 2!19.9
TORQUE o.o o.o o.o o.o -o.o o.o o.o o.o o.o o.o o.o o.o o.o .o .. o o.o ..... HP 0.02 0.01 0.01 0.01 o.oo . 0.01 o~oo o.oo o.oo -OaOO o.oo OoOO
+:"" 0 .. 01 0.02 - 0.01 0
TABLR VI (Continued)
DATE 04/26 -04/26 04/26 04/26 04/26 04/26 04/2·6 04/26 04/26 04/26 04/26 04/26 04/26· ·04/26 04./26 TIME 1245 1310 1325 1345 1400 1419 1435 1447 1505 1530 1545 1605 - 1625 1645 1701
l TCll 142024 146•40 150.28 157.93 168,44 174.31 172.56 165.69 158.8_3 -141.39 139.80 139.09 138.38 137.87 136. 89
T(21 l-4-8.25 152-."30 156..01 163014 172.26 177 .45 176.08. 170.25 l63.91 146.87 145~01 144.03· ·- 142. 71 141.50 139.70
Tl31 154-.59 158. 70 162.06 168.14 l 75.6i. n<i. n 178.82 174.64 168.88 153.11 151.16 150004 148.29 146046 ll't3~80
T(41 158.-46 161.26 164.1-.8 169. 51 175.51 179.32 178.66 175.31 - 169.95 155.84 154.02 152. 91t 151.22 -149.37 147.00
Tl5l 160.41 163. 78 166.09 170.39 175.08 177.89 177.49 175.44 -170• 92. 159 .oo 157.49 156.31 154.46 152.94 'isl.OS
T(61 159.-88 -162.43 164.38 168.88 172.40 173.97 173.30 111. 76 167.90 157.99 156.85 155.43 154.49 - 153.25 152.-00
158.06 162043 155.13 ·,·:.
TUI 160.75 165.45 168.58 171.39 170.89 169.38 165.86 157.15 156.01 154.12 152.98 15_1. 76
·u e, - 154.02 156.41 157.96 160.55 163.44 166.56 165. 7(, • ·- l.64.-21_ 161.02 153.18 152.30 151.42 150.55 .-149.70 148".-69 . 159.s4 i;J'.6~ . 154.69 147.51 145.32 T(91 148.22. · 150.28 151.66 154.12 157.39 161.05 146.70 146.06 144.57 144 •. oo
T( 101 140.79 142.51 143.86 146.40 150.62 155.17 153.45 150.08 i.47.07 140.56 139.84 139.43 139.23 138.92 138.89
H 111 133.57 . 135.06 136.59 139.53 144.98 150.41 155.00 143.66 1.40.45 133.81 133.27 134.86 133047 133.67 134.35
TEil q2.26 92.13 92.16 92.06 90.61 90.30 90.82 91.71 92.09 93.92 94.02 94.19 95.09 .. , 95.74 --- 96~46'
TEI 97 •. 05- 96.06 95.89 95.75 94.13 91.44 92.58 95.37 · q6.02 99.05 99.80 -100.42· 102.00 102.41 104.47
TEO 101.86 102.03- 101~00 100.73 q5.e2 92.68 94.20 101.25 l"00.90 '104.13 104.44 104.98 106.73 108.37 109.64
T.EDL 103.27 102.94 102~77 102.56 101.10 100.81 101.37 102.52 102.63 104.78 105.15 105.53 107.12 108.43 109.63.
TRATIO 0.-44 0.36 o .• 3,5 0:35 0.34 0.11 0.17 0.34 o.3i 0.47 0.52 0~55 o.s1 o.53 Oo6l
Ql 54.32 56.55 58.91 63031 '-68.39 71.68 71.10 6Be21 63.68 52.26 50.84 50.00 48.68 47.27 45.49
Q 1340.06 1319.95 1315.87 131"3.18 1308.11 1304.81 1318.80 1347.63 1311.U 1296.96 1325.66 1326049 1345.70 1348.83 1325.88
Ht 9.08 8.68 8.32 a_.21 7.59 6.72 6.69 7.U 7.51 9.74 10.60 10.74 12.40 13.42 14.62
'AGRPM 216031 177.62 138_.63 98.-89 59·.76 -_38.73 - 47.6i 77.Yt 96.43 255.43 297._56 336.85 420.06 50~.47 587.50
RER 213.6 171. 7 133.2 94.3 53.9 33.4 42.3 73.3 92.5 268.2 318.3 366.4 483 .. 5 . 598.9 738.3
WlBH · 259.9 258.4 258.4 260"'0 25"8.7 257.2 ..
258.6 258.5 2"58s4 258.l 259 .. 6 258.0 253.2 248.t 245.1
TORQUE o.o 1).0 -o .• o -o.o o .. o o.o o.o o .. o OaO o.o o .. o o.o o.o o .. o o.o I-'
HP\_ 0.01 0.01 o.oo o.oo 0~00 o.oo o.oo o.oo +='"' o~oo o .. m~ tloOZ Oe03 o.o.i. 0 .. 06 0.09 I-'
TABLE VI (Continued)
DATE 04/26 04/26 04/26 04/26 04126 04/26 04/26 04/26 04/26 04/26 04/27 04/27 04/27 04/27 04/27 TIME 1721 1740 1800 1815 i830 1841 1850 1900 l9i5 1937 .1550 1607 1622 1642 1700
TUI 136.55 135.84 129.46 128.92 129.23 128.14 128.85 130.14 132.01 135.10 185.10 183.90 HI0;.83 177.08 167.94
T<21 138.35 136.82 128.55 128.58 ·129.43 128.44 129.16 130.45 131.57 135.20 189.81 188.11 183.00 178.15 167.27·
T< 3 I 140.92 137.94 129.06 127.77 128.58 128.21 128.89 130.28 130.75 136.62 196.14 193.18 1.85.04 i78.59 167.13
Tl4) 143.42 139.13 13-0.79 128.85 128.27 127.70 128.44 129.67 131.60 138.62 199.50 196.54. 186.11 178.66 H,8.41
T(5) 146.33 139.94 132.15 129.77 128.14 126.47 127.19 128.72 132.45 139.50 203.65 200073 186.84 178;.22 168.61
Tl6l 147.34 140.48 133.54 131.16 128.12 125.83 125.93 127.56 133.27 139.77 203.95 201.19 189. 71 178.69 169.48
T(7) 147.54 141. 29 134.86 132.65 129.67 125.66 125.01 126.41 134.18 141.09 201.39 198.73 187. 61 179.32 171.36
Tl 8) 145.59 140.55 135. 27 133.30 130. HI 125.35 124.67 125.90 134.52 141.12 196.41 l93.-CJ7 185.27 178~36 171.9.6
Tl91 141.83 138.62 134.08 132.42 129.63 125.22 124.84 125~83 · 133.81 139.43 189.84 187.84 .181.16 176.ll 111.02
TUOJ· 137.77 136.18 132. 72 . 131 • .30 128.99 125.42 124.74 125;56 132 •. 99 137.47 182.53 181.43 176.92 173.6.0 169.72
T( 111 134.01 133. 50 130.99 129.80 127.94 124.54 123.82 124.50 131.70 135.33 175.98 175.31 172023 170.22 167.23
TEI.L 97.35 99.07 101.61 102.50 103.40 104.73 105.73 · 106.68 105.35 103.81 122.77 123031 124.23 125.22 · 126.44
'.fEJ 106.22 108. 79 111.21 111:.86 112.6,; 115.38 116.99 118.97 114.22 112.75 127.21 128.77 129. 72 132.47 134.13·
TEO lll.35 113 .Bl 117.33 118.56 119.99 121~90 123.46 125. 30 i20.53 UB.35 135.46 136.51 138.37 140.40 142.43 1·
TEOL 111.56 115.16 116. 73 117.69 118.98 120.79 122~39 124.16 119.87 118.51 138.62 139.50 145.99 145.55 142.51
TRATJO 0.62 0.60 0.64 0.62 o.59 0.66 0.68 0.10 Oo6l 0.61 o. 28 0.34 0.25 0.36 0.48
.Ql -42.83 39.71 33.84 32.52 32.13 31.74 32.24 33.08 34.41 39.34 90.05 87~25 77.68 11 •. 10 62.39
Q 1.358.80 1368·.16· 1355.37 1356.69 1341.97 1342.37 1332.<)7 1327.71 1328.08 1325.117 1871. 77 1874.56 1895.61.1896.86 1920.34
HC 18.43 25.72 41.28 52.11 63.34 83.76 89.53 96.68 48 •. 44 27.54 12.77 n. 12. 22.67 26.57 33.li2
AGRPM 672.53 750.83 -a31.15 873. 75 917.50 978.91 1016.92 1111.60 808.68 'fl<J.97 225.92 . 265.16 306.59 347.55 388.43
RER 901.3 1122. 3 1332.9 1429.2 1556.0 1778.5 .1943.8 2250.9 1422.6 1210. 5 656.5 795.5 1040.0 1202.1 1295.9
WLBH 244.0 249.0 248.8 245.8 248.4 24802 247.9 249.l 248.3 z4e.;s 23·5.9 234.4 232.2 232.3 . 232.1'
TORQUE o.o o.o o.o o.o o.o o.o o.o ·o.o o.o o.o .o.o o.o o.o. o.o o.o. f->
HP 0.11 o.u 0.19 0.22 0.24 0.29 0.32 o.n o.n o.n o.oo 0.01 0.01 0.02 0.02 ~ l\)
TABLE VI (Continued)
DATE 04/27 04/27 04/27 04/27 04/27 04127 04/27 04/27 04127 04/27 05/14 05/14 05/14 05/14 05/14 TIME 1715 1730 1750 1810 1822 1837 1850 1900 1910 1915 1445 1520 1605 1640 : 1710
T 11 I 160.72 157.59 157. 56 157.96 157.99 159.20 160.31 161.56 163.10 163. 54 170.08 172. 70 165.05 160.18 147.85
Tl21 161. 39 158.16 158.16 158.53 158.46 159.71 160.75 162.03 163.67 164.04 173. 74 177.69 167.64 160.85 147.24
Tl 31 160.72 157.86 157. 93 158.46 158.46 159. 71 160.75 161.99 163.78 164'. 31 178.96 184.34 171.46 161.26 lft5.Dl
Tl41 160.68 157.25 157.5 2 158.03 158. 13 159.47 160.52 161.86 163. 71 164.11 183.10 187.04 175 •. 44 161.59 145.35
Tl 51 160. 2 5 155.50 1 55. 94 156.81 156.95 158 .4'0 159.51 160.85 162. 77 163.20 186.84 192.04 178.96 162.03 '146. 73.
Tl 61 H,1.02 154. 76 154.36 155.33 155.50 157.32 158.50 160.04 161.89 162.50 187.84 192.51 180.06 163.04 147.75
Tl 71 162.43 154.32 153. OB 154.19 154 .66 156.21 157~49 159.07 161.02. 161.56 185.81 189.94 178.49 163.74 150.28
Tl 8) H,2.94 154.93 152.23 153. 28 153.99 155.50 156.8 l . 158.33 160.21 160.85 181.20 185.04 174.61 162.40 151.86
T(91 162. 77 155.10 152.07 153.08 153. 78 155.10 156.48 158.03 159.84 160.48 174. 81 178.12 168.88 ·159.a1 151.56
TllOI 162.40 155.40 151.76 152.57 153.45 154.83 156.0l 157.69 159.51 160.15 167. 84 169.88 163.04 156.95 150.65
Tl 111 161. 02 153.82 150.04 150.95 151~93 153.25 154.76 156.38 158.23 158.93 161. 22 162.06 157.45 153.35 1'>!1.52 ·
TEil 127.90 128.78 129. 91 131.03 131.77 132.99 134.01 135.67 136.42 137.60 107.95 l 06. 79 106.92 107.37 108.67
TEI 134. 34 136.85 138. 91 141.52 143.41 145.78 147.91 150.40 152.ft3 153.88 116.65 114.43 116. 20 118.45 120 •. l&
TEO 144.60 145.85 147.50 149.05 150.23· 152.06 153.91 156.07 158.09 159.47 124.59 122.10 124.45 125. Bl 128 .. 74
TEOL 144.07 145.18 146.57 148.19 149.20 151.12 152 ~ 91 155.00 157.12 158~19 125.07 123.16 124.08 127.60 127.73
TRATIO 0.40 0.49 o.54 0.61 0.67 o. 71 0.74 o.76 o.77 o.79 o. 51 0.47 0.54 0.55 Oo60
QL 56.09 53.37 53.58 53.98 54.06 . 55. l 3 55.96 57.04 58. 53 58.86 75.00 7.8.52 68.33 56.82 H. 26 •
0 1926.6.5 1946.27 1949.36 1958.90 1958.82 1930e08 1942.86 1926.94 .1925.44 1923.05 1911.39 1905.82 1913.96 l<JU.52 1942.13
HC 51.70 70.68 74. 77 83.89 93.41 99.50 109.83 12!.49 123.91 139.31 13.89 13~02 15.82 27.14 4~.08
AGRPM 450.59 512.14 ·597. 15 685.86 767.56 '855.30 941.48 1018.33 1095.59 1164.48 342.66 261. l'i 424.90 510.44 635.811
RER 1547.2 1836.7 2236.2 2704.7 3132.9 3681.4 4251.7 4860. 7 5502.3 . 6021. 8 688.5 492.5 832. 1 1099.2 llt99 .. 1
WLBH 232.5 231. 0 229.6 226.'11 224.4 22.-..1 225.0 223.5 223.2 223. l 232.8 239.5 236.a 23i'o!l 237 .. 5
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o f-' ,-. HP 0.03 0.04 0.06 o.oa o. rn o.n o.Ul 0.21 . 0.25 Oe2~ 0.02 0.01 0.03 CL:i[l)~ o.oa G.,
TABLE VI (Continued)
DATE 05/14 05/14. 05/14 05/14 05114 05/17 05/17 05/17 05/17 05/17 05/17 05/17 05/17 05/17 05/17 TIHE 1745 1800 1835 1855 1q15 1140 1528 1631 1705 1748 1816 1915 1937 2015 2042
Till 142 .9.8 143.39 146.40 146.40 147.92 139.64 140.31 166.90 160.62 155.10 151.36 148.59 147.00 162.06 145.21
Tt21 142.82 143,2q 146.60 146.50 148.09 143.80 144.37 171.42 164.75 159. 71 156.07 153. 31 151. 63 166.23 149.43
Tl31 142.38 142.95 146.36 146.33 147.81 148.52 149.23 172.77 168.78 164,61 161.39 158.80 156.88 17().29 154.29.
Tl4l 141.50 141.80 145.76 145.55 147.21 151.42 152.30 173.44 170.45 167.13 164.41 162.06 160.38 171.93 157.69
TC51 139.97 140.41 144,71 144.34 146.16 153.75 154.66 172.46 · 170.42 167. 77 165. 52 163.57 162.20 172.13 15.9.67
TC 61 139.06 139.40 143.5 2 . 143. 05 145,·os 153.75 154.79 170. 39 168.91 IM. 76 164. 85 163.34 162.13 170.75 159.74
Tl71 138. 76 138,92 142,41 141.83 143,80 151.8_0 153.11 166.90 165.69 163.91 162.40 161.19 160.08 167.70 157.99
Tf 81 138. 79 138.96 141.. 77 141,16 143.19 148.52 149.70 162.53 161.49 160.01 1511. 83 157.49 . 156.61 163.51 154.56
Tl 91. 138.92 138.96 . 141, 39 140.82 142.75 143.52 .144.71. 157.25 155.94 154.49 153. 75 i52.57 151.56 158-06 149.47
TllOI 138.82 138.89 140.99 140 .• 28 142.34 ·137 .54, 138.69 151.39 149.23 147.65 147.07 145.99 145.08 151-59 143036
Tl 111 137.13 137.40 139.36 .138.65 140.79 131.77 132.96 146.40 143.66 141.67 140.95 1'39. 80 138,99 146,06 137.64
TEil 110,93 111,37 116,39 116,05 111.55 95.33 92,95 91.92 92,33 93,19 94,50 94.02 94.36 94,40 95.39
TEI 122.85 123,33 132.06 130.09 133.59 102.03 102.21 95,85 98,26 99,67 101. 59 102,03 103,44 100.73 lOlt,81
TEO 131,59 132.03 138. 54 137.29 140.06 109,50 111. 35 104.09 107. 21 109.33 111,52 112, 72 113.91 110 .• 02 lllt,67
TEOL 130,52 131, 13 137,43 136,35 138.96 110.95 110,85 109,07 109,81 111,04 113,58. ll3,31t 113.56 112.92 115,07
. TRATIO 0.61 0,61 o •. 74 · 0.69 0.75 0,43 0.52 0.23 0,34 0.36 o. 37 0.41 0,47 0,34 0,48
Ql 41.42 41,64 44.56 44,41 45.64 48.84 49.51 66,62 64.10 61.34 59.11 57.20 55. 85 . 65.34 53,71
Q 1944.97 196'1.64 1q62.·05 1966,32 1967.14 957.30 959,53 943.88 960.84 971.32 973.55 975,46 975,31t 961,06 976.55
HC 77.56 79,88 102,29 92.20 103.5q 8.65 8.49 5.64 5.85 6.15 6.58 7,00 7,25 6.07 8.07
· AGRPM 762.46 760.90 1075,94 927.70 .1073.61 217.47 217.17 43.37 62.01 82.01 100.79 120,58 139.51 60,74 178.'62
RER 1822, 2 1849.l 3216.l 2665.4 3348,4 272.8 272,7 48,2. 72,3 100. o 133.2 159.4 188,6 78.~ 253,8
Wl8H 238.4 235. 7 244. l 237,5 243.q 131. 7 115.0 113,9 113.8 1,12.8 105.8 104.~ 105.5 101.1 103.2
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o. o.o o.o o.o o.o o.o o.o o.o ...... HP 0.12 0.12 0.21 0.19 0.27 0.01 0.01 o.oo o.oo o.oo o.oo 0,00 o.oo o.oo o.oo
.i:--
.i:--
TABLE VI (Continued)
DATE 05/17 05/17 05/17 05117 05/17 05/17 05/17 05/17 05/17 05117 05/17 05117 05117 05/17 05/17 TIME 2100 2130 2150 2213 2230 2245 2300 2315 2330 1748 1816 1915 1937 2015 2042
Tl 11 143.86 141.77 143.19 139. 16 141.43 138.15 131.84 132.28 132.99 155.10 151.36 148.59 147.00 162.06 145.21
H21 147.81 144.37 146.40 140.08 143.09 138.59 131.57 132.35 133.03 159.71 156. 07 153.31 151.63 166.23 149.43
TC31 152.44 147.95 150. 55 141.46 145.6,9 · 139.40 131.13 132.15 132069 164.61 161. 39 158. 80 156.88 170.29 .154.29
Tl41 155. 81 150.95 153.51 143.12 148.31', 140.48 131.6·0 131~60 132.01 167.13 164.41 162. 06 160.38 171.93 157.69
Tl 5) 157 .82 153. 31 155.84 145.15 150.99 141.16 132.01 130.48 130. 79 167.77 165.52 163.57 162. 20 172.13 159.67
Tl61 158.06 154.36 156. 58 147.41 152.60 141.29 132.62 129.16 129.40 166.76 164. 85 163.34 162.13 170.75 159.74
Tl71 156. 31 153.31 154.96 147.58 152.23 141.67 133.91 128.14 128. 72 163.91 i62.40 161.19 160.08 167.70 157.99
T(8) 152.98 150.38 151.73 145.65 149.87 140.62 133.64 127.80 128.31 160.01 158.83 157.49 156.61 163.51 154.56
Tl91 147.95 145.79 146.87 142.38 146.03 138.11 · 132~35 127. 77 '1.28. 55 154.49 153.75 152.57 151.56 ,158.06 149.47
T( 10) 142.00 146.70 141.29 139.13 141.73 135.88 131.26 127.56 ·12a.-55 147.65 147.07 145.99 145.08 151.59 143.36
Tllll · 136.35 135.98 136. 21 136.08 lH.91 133. 71 129.97 126.68 127. 53 141.67 140.95 139.80 138. 99 146.06 137.64
TEIL 95.09 95 •. 'B 95.81 96.08 95.84 96.0l 96.50 97.49 98.69 93.19 94.50 94.02 94.36 94.40 95.39
TEI 105.57 108.24 108.07 112. 38 111. 56 114.39 115.96 121. 73 121.45 99.67 101.59 102.03 103.44 100.73 104.81
TEO 114.77 116.92 116.27 119. 78 1111.u, 121.08 123.97 128.36 128.43 109.33 111. 52 1J2.72 113.91 110.02 ll4.6_7
TEOL 114.38 116.65 117.82 120.67 119.-00 120.79 123. 11 127.36 127.53 111.04 113. 58 113. 34 113.56 112.92 . 115.07
TRATIO o.54 0.60 0.56 0.66 0.68 0.74 0.73 0.81 0.79 o._36 0.37 0.41 0.47 o.34 0~48
Ql 52.23 48.48 50.45 42.61 46.51 . 40.69 34.41 34.41 · 34.69 61.34 59.11 57.20 55.85 65.34 53.71
Q 978.03 981.78 1051.69 1065.90 1062.00 1069.40 1075.68 1086.82 1082.54 971.32 973. 55 975.46 975.34 961.06 976.55
HC 8.55 11.32 U.45 21.76 15. 35 23.25 49.90 93.34 88.06 . 6.15 6.58 7.00 7.25 6.07 8007
AGRPM 218.10 379.63 298.58 548.09 465.4-8 630.27 756.37 949.06 875.54 82.0l 100.79 120.58 139.51 60. 74- 178.62
RER 308.2 581. 8 468.0 959.l 779.6 1132.0 1449.5 2109. 3 · 1946.5 100.0 133.2 159.4- 188.6 78.3 253.8
WL8H 105.5 103~3 103.0_ - - 103.8 104.7 106.6 110.0 114.4 111.1 112.a_ 105.8 104.8 105~5 107.1 103.2
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o .. I-'
HP o.oo 0.03 0.02 0.-06 0.04 0.09 0.15 0.26 -0 .. 21 0~00 o.oo o .. oo o.oo o.oo o.oo +:""" \JI
TABLE. VII
DATA FOR HEAT TRANSFER TESTS WITH GULF 'HARMONY OIL 151 AND THE 4.000 INCH DIAME.TE.R BLADE.
DATE 09/15 09/15 09/15 09/15 09/15 09/15 09/15 09/15 09/15 09/15 09/15 09/15 09/15 09/15 09/15 TIME 1120 1155 1220 1245 1310 1340 1400 1425 · 1455 1525 1540 1600 1635 1650 1720
T( 1) 104.53 113.70 106.45 107.16 l 06. 10 108.09 107.85 104.01 108.81 104.05 103.05 102.81 114. 41 119. 70 108.46
Tf 21 112.4_3 120 .• % 112.57 113.63 112. 02 114.89 116.29 111. 75 118.17 111. 85 110.69 110.28 124.36 116.67 117.86.
T(3l 114.62 122.60 114.58 115.98 113.93 118.88 118 .• 57 115.27 120.25 113. 73 112. 36 l ll. 92 125.22 -118.88 119.90
T( 4) 117.28 123.68 116.53 116.49 115. 98 119.22 120.38 115.57 121.Bl 115.64 114.31 113.87 125.69 120.55 121.44
T(5) 117.38 123.65 117.38 118.88 117..31 119. 73 120. 82 '116.15 121.57 116.29 115.10 115.10 125.39 120.82 121.64
T(6l Tl6.56· 121.98 116.67 117.72 114.82 117.21 H8.i3 . 114. 65 119.09 114.58 113. 63 113.25 122. 53 118. 71 119.56
T'71 114.75 120.38 .114.82 116.12 114.41 116.70 111.82 114.00 118._68 113.97 113.ll 112. 77 121.57 111.12 118.57
T(81 112.43 117.86 112·'43 113.63 .112.06 114.24 115.33 111. 78 116.26 111.11 111 •. 00 110.65 118.95 115.16 116.09
T(9J 109.70 115.64 110.89 112.02 110.69 112.57 113.5q 110. 31 ·114.28 110.21 109.49 1Q9. ll 116.87 113.22 114.11
Tl 101 109.35 113. 25 110.04 110.55 109. 53 111.10 111.95 109.15 112.40 109.15 10Bi43 108.12 114.11 111.47 1_12.06
T( 11) 107.61 110. 86 108.09 l OB. 77 107.92 109.18 109.83 107.75 110.38 107. 78 107. 23 1.08.50 111. 85 109.49 109.87
TEH. 95.26 9<t. 91 95.95 95.77 96.15 95.95 95.91 96.46 95.43 95.98 q5.95 95.91. 94.91 95.33 94 .. 23
'TEI 96.88 96.23 97.60 97.05 97.91 97.16 97.23 97.91 96.95 97.30 97.30 97.30 95.11 96.26 95.20
TEO 98,26 96.44 99.97 q9.33 98.50 96.33 98. 29' 101. 04 91'.;23 100.35 100.49 100 •. 66 96.26 97.26 95.54·,
TEOL 98.82 96.28 99.58 99.30 ·99. 75 99.41 99.35 100. 11 98.84 99.61 99.66 99.67 98.28 98. f)5 97.66
TRATIO 0.46 0.39 0.46 0.36 0.49 0.35 0.38 0.40 0.45 0.36 0.36 0.37 0.24 0.28 0.28
QL 24.90 29.06 24.43 24.41 24.08 26.15 26.90 23.83 27.83 23.87 23.03 22. 76. 30.39 27.0l 27.58
-0 814. 21 810. 84 8 30.00 818.97 619.29 815.10 914.35 817 oc42 814.77 825.70 624.40 828.17 810. 86 802.50 825.49
HC 15.21 12.16 1.8.30 16.68 14.52 15.12 ll. 71 21.55 U.51 17.04 16. 87 18.36 10.50 12.00 11.83
AGRPM 148.17 55.75 170.06 132.38 169.41 114.05 94.70 210.36 17.06 189.41 229. 13 2411.07 41.55 86.30 70.50
RER 143. 3 52.7 .169. l 129.8 189.9 112.2 93.1 212.7 74.6 187.7 227.3 246.l 39.0 82.4 64.8
WLBH 507.9 515.2 512.4 512.5 516.0 . 'H4.9 514.9 512.2. 512.6 514.8 514.8 514.8 515.2 517.6 515.4
TORQUE o.o o.o o.o o.o o.o 0-.0 o.o o.o o.o o.o o.o o~o o.o o.o o.o f-'
0~02 +:'"'
HP. 0.01 o.oo 0.01 0.01 0.02 0.01 o.oo o.oo 0.02 .0.03 0.03 o .. oo o.oo o-.oo a-.
TABLE VII (Continued)
DATE 09/15 09/15 09/15 09/15 09/15 09/15 09115 09/15 09/15 09115 09/15 09/15 091.15 . 09/15 10/08 TIME 1745 UlOO 1820 1845 1900 1915 1935 1955 2012 2025 2040 2050 2100 21-05 1230
T(l l 109. 32 101.96 101.82 104.18 104. 83 105.38 106.21 106.27 106.79 106.62 104.01 104. 70 108.88 109.90 141.67
Tl 21 118.88 109.0l 109.0 l 109.70 111. 20 111.54 113.76" 114.11 11-4.41 114. 31 115.81 116.36 119. 70 120.45 145.89 .
Tt31 120.76 .110.55 110.65 111.85 114.11 114.14 116.15 116.84 116.15 116.15 117.31 117 •. 89 120.72 121.44 147.17
T(4l 122.08 112.57 112.74 114 .• 62 117.21 117 .18 119.02 119. 70 118.40 118.54 119.02 119.56 121.57 ·.121.95 148.36
TISI 122.12 .113.80 114.28 116.84 119.26 119.29 120.62 120.62 119.60 119.87 119. 73 120.38 122.15 122.46 149.03
tc 61 119.90 li2.60 113.46 116. 02 118.57 118.54 120.18 120.89 119. 77 119.90 120. 25 121.10 122.1.2 122.12 149~03
T(7) 118. 75 111.95 112.77 115. 57 118. 78 118.64 120.25 120.76 119. 70 119.90 120.04 120.72 121.64 121.85 147.75
TISI 116.12 109.56 109.97 111.95 115. 68 115.16 118.23 U8.57 l lB.03 118.00 118.40 119.05 120. 72 121.23 146.19 '
Tl9l 114.00 108.09 108.09 109.18 111.92 111.68 115.10 H5.to 115. 33 115.30 116.15 118.54 119. 77 120.42 144.84
TC 101 111.92 108.64 106.89 107.61 109.32 109.35 111. 711 111. 88 112.88 112.64 114.58 115.16 119. 19 119.94 144.10
TC 111 109.87 105.69 105. 59 106. 34 107. 78 107.99 l 09.-87 uo.oo 111.34 lU.17 113.29 113.80 118.17 118.54 142. l:l
TEI!- 94.09 94.95 95.1_2 95.95 96.80 97.15 98.18 98.66 99.42 99.38 100. 31 100.93 102.64 102.68 129~_57
TEI 95.06 95 .. 95 96.40 •n.23 98.33 98.64 100.01 100.22 101.97 101.55 104.5-'t 104.81 109.03 109.26 133.96
TEO 95.06 99.49 100.18 101.07. 102. 31 102.58 104.4 7 104.30 106.25 105.98 108.27 108.61 112.14 112.14 137.25 ,~,,
TEOL 97.48 98.83 99.16 100.15 101.55 101.45 103.16 103.42 104.98 104.74 106.77 107.05 111.06 111.44 133 .• 45
TRATIO 0.29 0.26 0.32 o·.30 0.32 0.35 o.37 0.33 0.46 0.41 o·.65 0.6.3 o.76 o.75 1.13
Ol 28.0l 21.95 22.06 23.23 24.86 24.84 26.02 26.46 25.62 25.71 26.02 26.37 27.67 27.92 46.51
0 825.06 835.99 831.01 821.50 819.87 819.89 823.55 823.11. 813. 25 823. 86 821.41 821.06 819. 76 819.51 827.48
HC ll.59 20.36 21.01 17.56 15.89 15.93 17.05 18.44 22.77 21.73 28.45 28.44 31t.Ol 34.07 25.60
AGRPH 70.50 285.13 325.87 366.60 525.46 406.31 525.46 497.97 604.89 574.34 702.65 678.21 861. 51 861.51 305.50
RER 64.4 272.2 315.5 367.6 552.7 . 428. l 586.9 561.0 122.1 678.-8 903.8 881.1 1.289.3 1303.7 945.;2
WlRH 521.6 521.2 518. 0 51-7. 7 517.2 519.l 518.5 518.5 5130 l 513._2 512.5 5i2.4 493.7 · 493.6 470.7
TORQUE o.o o.o o.o o.o o.o o.o o.o. o.o o.o o.o o.o o.o o.o o.o o.o. .!-'
HP o.oo .0.04 0.05 o.oa 0.11 0.0_<.1 0.15 o.u 0.20 O.HI 0.29 o.:u, 0.42 0.42 0.02 +--.J
TABLE VII .. (Continued)
DATE 10/08 10/08 10/08 10/08 10/08 10/08 10/08 10/08 10/08 10/08 10/08 10/09 10/09 i0/09 10/09 TIME 1310 1345 1410 1437 1455 1525 1600 1625 .1640 1715 1735 1410 · 1430. 1453 1720
Tl 11 140.58 141.12 141.39 142. 27 143.12 147.85 152. 81 140.24 146.36 147.68 146. 70 147.21 149. 37 152.50 157.99
Tl 21 146.53 141.07 147.68 148.89 150.14 156 .11 160. 89 147.17 147.68 149.03 147.58 147.88 149.91 152.77 158 .. 36
Tf31 147.85 148.39 149.03 150.41 152.13 158.50 162.67 148.39 149.10 150.78 148. 36 148.15 150.11 152.98 158.36
TC4·1 148.93 149.43 150.04 151.42 153.11 159. 71 163.07 149.57 150.18 151.39 148.59. 148.42 1.50. 38 153.04• 158.4~
TISI 149.57 150.04 150.45 151. 63 153.48 159.74 162.83 150.14 15·0. 78 151.90 148.73 148.56 150.28 152 .. 94 158.43
Tl6l . 149.57 149.91 150.18 151.29 152.94 158.87 l 61. 56 150.21 150.;72 151.59 148.36 147.88 . 149.57 152.13; 157.52
Tl71 148.63 148.76 148.96 150.08 151.42 158.50 159.47 149.23 149050 150.38 147 •. 88 147.41 149.27. 151.66 157.29
T(RI 146.90 147.07 147.51 148.42 .149. 70 154.46 156.92 147.58 147. 75 148.89 147.54 146.90 148. 93 151.42 156.85
Tl91 145.5 9 145.82 146. l 9 147.17 148.09 152.13 154.29 146~23 146.53 147 .41 147.07 146.57 148.69 151.12 156.51
Tl 101 144.54 144.71 145.05 145.86 146.53 149.57 151.39 145.15 145.45 146.13 146.57 146.40 148. 22 150.78 15!>.61
Tl 111 142.85 143.19 143.32 143. 86 144.47 146.90 148.42 143.46 143;.63 144.20 145. 21 145.48 147. 34 149.87 155. 33
TEf.l. 130. 41 130. 99 131.30 131.26 130.79 130.28 129 •. 91 · 131.43 131.53 131.60 131. 50 i33.50 136.18 139.09 · 145.48
TEI 134.78 135. 18 135.35 135.83 135.63 135.18 134.81 136.00 136.17 136.34 138. 37 140.40 143.95 147.03 15:3.61
TEO 138 .• 20 138.40 138.5.7 138.95 138.54 135.66 i34.68 139.42 139.72 139.39 140.74 142.57 146.0l 149.43 156.67
TEOL 137.26 134.60 13'+. 86 134.75 134.18 133.58 133~24 138.28 135.12 135.12 139.47 141.33 · 144.71 148.25 155.30
TRATIO 0.64 1.16 1.14 1.31 1.43 1.49 l.47 0.67 l.29 1.35 0.86 0.88 0.91 0.87 0.83
QL 46.94 47.32 47. 7·8 48.84 '50.13 55.31 58.01 47.42 47.89 48.81 46.68 46.56 48.04 50.08 54.32
Q 825.68 825.30 827.58 826.52 825.23 806.33 817.35 827.94 827.48 826.55 828. 68 822.52 842.15 840.ll 821.04
HC 30.12 25.74 25.10 23.11 19.99 13.32 12.40 31.29 · 25.82 24.57 42.49 52.23 67.96 71.81 103.25
AGRPM .305. 50 259.06 218. 94 179 .• 63 139.31 62.32 35.90 296.33 238. 29 179r02 418.53 549.90 672.10 .· 794.30 953.16
RER 1020.3 828.5 704.7 579.9 444.2 195.7 lll.6 1020.0 777.0 584. 8 1505.9 2084.3 2791.1 3599., .· 5!27.3
Wt.BH 496.0 494.8 494. 7 500.6 500.7 5-00.9 501.0 494.2 495.2 495.2 493 •. 9 488.7 487.7 4;88. 8 ,486.6
TORQUE o.o o.o o.o o.o o.o o.o o .• o ·o.o o.o, o.o o.o -o.o o.o o.o OoO . I-'
HP 0.02 0.02 0.01 . o. 01 o.oo o~oo o.oo 0.02 0.01 0.01 o.os o.oe 0.14 0.19 0.27 +:-O',).
TABLE VII (Continued)
DATE 02118 02118 02118 02/18 02118 0211!1 02/18 02/18 02/18 02118 02118 02/18 02/18 .02/18 021i8 TIME 1620 1632 1650 170.5 1725 1742 1755 1810 1828 1845 1900 1915 1925 1935 1955
Tl 11 143.63 143. 63 143.96 144.27 142.10 142.04 141.97 142.51 143.36 143.4.9 142.61 142.51 142. 21 32.37 146.03
T{ 21 147.44 147.41 147.58 147.61 144.54 143.86 143.56 144.00 144. 51 144.47 143~ 32 142.88 142.9.5 32.37 148.29
Tl 31 151.80 151. 73 151.90 152.13 148.91 146.84 146.19 146.06 145.92 145.01 143.66 143.19 142.98 32.37 152.44
Tl4l 156. 31 153 .14 155.13 155. 50 152.34 149.23 154.90 147.54 146.57 145.38 143.96 143.49 143.46 143.46 156.18
Tl5) 158.97 158.87 159.64 159.71 155.84 151.76. 149.74 148. 29 146.43 144.67 143.36 142.82 142.75 142.78 159.37
Tl61 1.59.84 159.71 160. 95 161.05 159.20 152.23 150.11 148.42 146.26 144.54 143 .• 15 142.48 142.21 142~17 161.02
Tl7l 157.66 157.62 159. 00 159.57 155.91 150~78 148~96 147.51 145.65 144.03 142.65 141.53 141.36 141.19 159. 34
TISI 153.08 152.91 155.00 155.03 152.34 147.71 146.23 145.18 145.89 143.49 . 142. 31 141.29 14.0. 82 32.37 155.91
TC'll 146.57 146.19. 149.60 149.64 147.61 143.69 142. 51 142;,27 142.68 142.98 142. 21 141.09 140.65 32.37 150.92
Tl 101 l39.97 139.60 142.78 142.9!1 141.83 139.06 138.62 139.60 141.16 142.17 142.14 140.85 140.31 32 .. 37 145.38
Tl 111: . 134.42 134. U! · 136. 69 136.89 136.59 134.89 135.13 136. 72 138.55 139.91 140.08 139. 94 139.09 32.37 140.41 ·
THL 106.27 106.31 108.64 107.13. 108.33 109.01 109.35 110.14 110.86 112.06 112. 74 113 .52 114.31 114.79 111.05
TEI 107.35 107.42 lOR.37 100. 55 109.74 ll0.87 111.86 114.63 117.29 119.31 120.64 122.14 123.43 12(>.28 ll3.03
TEO 116.92 117.12 118.11 118. 11 119.51 120.40 120.94 121 •. 93 123.12 124.35 125. 20 126.32 127.27 128~09 122.54 ..
TEOL 117.85 117.96 120.38 118.94 120.21 121.10 121.69 121.81 123.00 124~30 124.67 125.52 126.41 127.19 123.42
TRATICI 0.09 0.10 o.oo 0.12 0.12 0.15 0.20 o.38 0.53 0.59 0.66 0.12 o.75 0.77 ·0.10
Ql 52.63 .50.16 51. 70 51.99 49.54 .47.17 51.52 45.90 45.16 44.28 43.23 42.88 42.86 42.86 52.52·
.g 2078.78 2091.05 2085.25 2100.36 2087.42 2089.79 2081.18 2091.06 2086.24 2050.64 2056.76 2076.61 2076.64 2073.23 2052;.98
HC 21.62 25.42 24.43 23.91 28.75 30.59 22.46 36.05 41.18 46.39 51.28 · 55.89 58.52 -183.32 25.90
AGRPM 339.10 339.10 ·378. 82 3 78. 82 415.48 '458.25 497.97 543.79 583.50 626.27 662.93 702.65 739. 31 775.97 381.88
RER 574.8 576.7 685.3 666.5 762.l 1166 •. 6 964.3 1090.l i.235.Z . 1391.5 1506.2 1650.5 1792.l 1921.3 ~76.3
WLBH 388.0 388. 0 387.4 387.7 387.4 387.2 H7.0 387.0 386.7 .386.4 386.3 386.l 385.,9 . 385.7 386.6
TORQUE o.o o.o o.o o.o o.o o.o o.o . o.o o.o o.o o.o o~o o.o o.o ·O.O· ..... HP 0.03 0.03 0.04 o. 04 0.05 0.06 0.09 o.n .. . 0.12 O. H 0.16 0.19 0.21 0.23 0.04
~
'°
TABLE VII (Cont:i,nued)
DATE 02/18 02/18 02/18 02/18 02/18 02/18 02118 02/18 02118 02/18 02/18 02/18 02/18 02120 02/20 TIME 2035 2050 2105 2108 2122 2135 2147 2159 2213 2230 2245 2250 2305 1300 1430
. Tl 11 146.57 146.26 145.45 144. 74 144.67 144.84 144.64 145.21 145.01 144.47 143. 80 143.56 143.83 167.23 169.48
Tf 21 150 .14 149.40 147.98 146.70 146.50 146.43 149.30 146.90 146.13 145.25 144.57 144.20 144.67 168.21 170.15
T(3) 156.38 155,33 151.96 149.43 148,86 148.39 147.41 149.06 147,00 145.72 144,£4 144.37 144.81 168.61 170.29
T(4) 161.52 160.68 156.28 152.07 150.99 149. 87 148.19 150. 7.2 147.17 145.69 144.91 144.51 144. 84 168.71 169.88
Tl51 165.22 164. 35 159.07 153. 92 152.27 150.45 148.19 151.63 · l't6.87 145.42• 144,54 144, 13 144,47 168.07 16_9,55 ·
Tl 6) 1~6.09 165,96 160.48 154.15 152.·74 150. 72 148.19 151~76 146.70 145,18 144.30 143.56 144,03 167.54 169.61
Tf71 l!,3,74 163,47 158. 80 153. 18 151,76 149.9_4 147,75 150,92 146.23 144.57 143,49 1'+2.112 143, 02 167.13 168,88
T(81 158,63 159,14 155.03 150, OB 148,89 147.H 145.89 148.52 145.38 144.23 142.98 142.21 142.17 166.56 167,90
Tl91. 152.20 153. 28 149.97 146.13 145,01 144.20 144.07 145.05 144.67 144, 17 142. 85 i41.77 141.94 166. 23 167,10
TllOI 145.08 146.03 143.56 142,48 140.62 141.50. 142.31 141,83 144.07 143,90 142,68 141-, 87 141.67 165. 79 166,09
Tl l ll 139, 23 140, ll 138.35 .136.69 136. 93 138.59 139.84 138, 76 141,43 142.07 141.29 140.28 140.0B 164.04 163.88
:rpl 108.81 109, ll 109.70 110.00 110.01 110, 31 110. 72 110, 72 l ll. 58 111,118 . 112.53 113.22 114.11 142.51 142.78
TEI 110 ,29 ll0.98 111. 69 112,48 113.44 116,58 1113. 45 ll6. 10 120,50 122.14 123.80 125.40 126,70 152,93 151,79
TEO 121,56 122,07 122,68 123.60 124,11 124,48 125,13 124.76 126,25 127,00 127.78 129.07 130.60 157.04 157,28
TEOL 122,82 123,06 123.98 124.44 124,69 124.30 125,35 124,81 126,20 126,44 127,02 · 128,21 129.60 156.34 156.81
TRATIO 0.11 0,13 0.14 0,17 0,23 0,45 0.5.3 0,38 0,61 0,70 0,78 0,81 0,81 0.75 0,64
Ql 56,77 56,09 52,60 49,33 48,50 47,66 46,38 48.30 45,62 44,51 43,93 43~63 43,88 62,64 63,62
Q 2082.32 2052.81 2070.31 2056.17 2045,99 2046,84 2031,65 2040,70 2045,49 2044,49 2045,07 2066.11 2065.86 1206.37 -1209.67
HC 20,42 21.11 25,32 29,72 32,24 35,49 40,48 33.96• 45.85 50~98 55,66 61.08 65,48 · 45,35 43,85
AGRPM 302,H 342.16 381.88 421. 59 464,36 5.07.13 546.85 484. 73 588.60 629.33 668,03 727._09 782.08 303.97 263. 75
RER 588. 5 674.3 .7-73. l 869.2 972.B 1092.6 1228,7 1049.2 1375,8 1504.8 1645-.2 1864.l 208'7.5 1651.9 1429.2
WLBH 31.5. 7 315.6 315.5 315.4 315.3 315.4 315.2 315.3 315.0 315.0 3l't.9 314.6 314.3 119.6 1.77.3
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o ·-0,0 ~
HP 0.02 0.03 0.04 0.05 0.07 0 •. 08 0.10 0.08 0.12 0.14 0.16 0.20 0.23 0.01 0.01 v, 0
7ABLE VII (Continued)
DATE 02/20 02/20 02/20 02/20 02/20 02/20 02/20 02/20 02/20 02/20 02/20 02120 02120 02120 02120 TIME 1505 1520 1535 1555 1610 1622 1635 1647 1702 1714 1725 1735 1740 1800 1810
Tl 11 169.51 170.75 168.98 168.54 168. ll 168.00 167.54 167.33 167.20 167.47 168.07 168.98 170.79 171.76 172.80
Tl21 170.65 172.16 170.22 169.41 168.88 168.94 168.14 167.77 167.54 167.80 168.41 169.21 170.89 172.06 173.10
TC 31 1 71. 83 173.97 171. 06 169.88 169.U 168.91 168.37 167.87 167.64 167.!lO 168.31 169.21 170.89 172.06 .173.10
T(4) 172.46 175. 31 171. 39 169.95 169. ll 168.91 l 68. 27 167.77 167.64 167.80 168.14 169 .15 170.92 171. 76 172.93
Tl 51 172. 60 176.28 171.02 169.41 168.64 168.44 167.87 167.20 167.03 167.07 167.54 168.47 170. 25 171.06 172.60
Tl6) 172.46 176.01 170.75 169~01 168.04 167.90 167.47 166.73 166.56 166.56 167.10 168.07 169.75 170.75 171.83 .;
T(7) 171.39 174. 71 169.88 lf,8.54 167.57 167.43 166.93 166.39 166.19 166.23 166.76 167.74 169.38 170.29 171.59
Tl8J 168.98 171.46 168.5_8 168.07 167 .13 166.86 166. 53 165.89 165.89 165.86 166.43 167.33 168.94 170.08 171.16
T(9) 167.13 167.74 168.94 167. 57 166.80 166.60 - 166,19 165. 52 · 165.42 165.55 166.13 167 .03 168. 61 169. 75 170.82
Tl 10) 165.59 164.92 166.23 167.00 166.43 166.19 165. 76 165.0.5 ·165.12 165.29 165.89 166.66 168.41 169.41 170.55
Tl 111 163.10 161.96 163.91 165.19 165.05 164.78 164.38 163.78 16"4.0l· 164.25 164.88 165.66 167.54 168.54 169.'72
TE[L 143.05 i43.49 143.80 144.00 144.03 144.07 144.17 144.44 144.67 145.08 146.16 146.80 148~22 1_48.96 150e04
TEI 150.37 147.87 152.06 1 !i3. 88 155.22 155.49 156.07 156.54 157.24 158.15 159.30 160.78 163.00 164.34 165.82
TEO 157_. 75 158.12 158.29 158.59 158.79 158.99 159.43 160.00 161.0l 162.06 163.20 164. 71 !66.93 168.37 169.88
TEOL 157 .52 157.52 157. 86 157. 82 158.06 158.30 158.56 159.17 160.18 161.09 162.30 163. 71 165.89 167.37 168. Ill
TRATIO 0.51 0.31 0.59 o. 71 O.BO o.eo 0.83 0.82 0.81 0.82 0.81 0.83 0.64 0.84 0.84
Ql 65.79 68.21 64.89 63.68 62.98 - 62. 81 62.28 61.86 61.75 61.89 62.17 63.01 64.49 65.20 66.19
0 1217.74 1229.56 ll67.86 1170.69 1174.62 1173.17 1174.69 1172.50 1172.61 1172.48 1172.20 1225.48 1205.16 1197.90 1196.91
HC 34.27 26.55 37.77 44.41 49.57 51.68 57.48 64.18 71.92 79.58 90.29 101.15 105.37 120.99 ne.n, AG RPM 2 23. 35 183.30 243.64 283.68 324.85 345.83 387.37 452.14 513. 24 578.92 639.51 704.18 769. 86 830.96 895.U
RER 1208.4 970.1 1344.·B 159-0.2 1849. 2 1980.3 2238.4 2647.5 3069.9 3537.6 4017 • 7 4573.6 "5257.9 5861.6 6523.5
WLBH 175.7 175. 7 175.7 175. 7 175. 7 175.6 175.6 175.5 175.4 175.3 175.2 175.0 174.8 1_74.6 114.4.
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o I-'
HP 0.01 o.oo 0.01 0.01 0.02 0.02 0.03 0.04 o.os o.cn 0.09 o..n o.n 0.11!. 0.19 \.n 1--'
TABLE VII (Continued)
DATE 06127 06127 06127 06/27 06/27 06/27 06/27 06/27. 06/27 06/27 06/27 06/27 07/04 07/04 07/04 TIME 1220 1245 1314 1340 1403 1425 1455 1528 1555 1630 1700 1730 1135 1200 1230
TU J 158.97 161. 09 162.5·0 158.03 154.56 151.83 150.62 151.26 152. 30 155.81 159. 71 163. 37 125.69 125.56 126.58
Tl2) 163.88 165.76 164.85 162. 57 157. 66 152.81 151.29 151.90 152.87 156.34 160.08 163.78 127. 39 127.05 128.27
Tl3) 170.39 170.59 165.99 168.94 162.87 154.32 151.83 152.07 153.14 156.48 160.28 163.78 129.60 , 129.26 uo.u
Tl4l 172.93 1 n.22 165.89 171.89 166.60 155.33 152.13 152.07 152.94 156.51 160.35 163.88 .130. 62 130.65 130. lt
Tl5) 176.31 171.69 164.08 175. 78 171.49 156.18 151.86 150.95 151.96 155.43 159.17 162.73 130. 82 130.75 130.11
Tl6) 175.48 169.48 163. 54 175.18 172.90 156.55 151.36 149.94 150.65 154.12 157.99 161.52 130. 31 130.41 129,fl
TI 7-l 171.49 164.68 162.03 111. 26 171. 89 155.43 149.97 148.02 148.09 151.96 156.14 15<J.74 128. 72 129.26 12e.;u,
TIS) 166.09 160.18 161. 15 165. 86 169.88 153.14 14 7. 5 8 144.71 145. 72 150.08 154.66 158.33 127. 77 128000 1.26.58
Tl9) 159.17 155.97 159. 71 158.83 · 163.98 148.12 143 .• 52 141.19 144.34 149.06 153. 78 157.49 124.84 124.88. 124.47
Tl 10) 150.28 150.55 155.03 150.11 156.18 139.60 137.81 138.18 143.09 148.19 152. 98 156.61 119.56 119~60 120.11
Tl 11) 139.94 142 .10 147.31 139.80 142.98 132.82 132.52 134.86 141.12 146.26 151.12 l.54.90 113.63 113. 73 114.96
TEil 114. 89 114.92 114.45 114.89 115.20 115.98 115.98 116.97 118.13 · 120.42 122.97 124 • .t,7 100.55 1 oo. 69 101.41
TEI 115. 72 115. 76 115.25 115. 69 116.58 119.34 122. 75 125.6~ 'l32.44 .137.79 143.11 147.97 101.55 rn1. 76 102.38
TEO 135.52 135.15 135.15 135. l 8 134.98 137. 35 137.86' 139.72 142.16 146. 39 151.35 156. 20 114. 53 114.87 115.04
TEOL 136.36 136.30 135.79 136.29 136.97 138.41 13~.90 138.82 141.09 145.48 150.45 155.20 114. 72 li4.75 115. 27
TRATIO 0.04 0.04 0.04 0.04 0.06 o.i5 0.30 0.40 0.62 0.69 0.73 0.16 0.01 0.00 0.07
Ql 66.19 64.75 60.31 65.31 60.89 51.86 49.38 49.33 50.00 52.TB 55. 82 58.67 33. 73 33. 75 33,1£1
0 2105.36 20~.04 2091.53 2091.10 2090.95 2010.57 2013.05 2013.10 2097.58 2102.51 2141.10 2111.011311.00.1312.901311.67·
HC 21.11 22. 87 29.18 21.23 25.29 43.30 55.15 59.42 12.20 78.38 RB. 94 98.57 30.04 .29. 83 34.04
AGRPM 133.17 1.00.01 61.59 136.98 175.47 253.12 334.29 454.73 574.09 M2.66 845.37 1001~ 74 229.36 · 22~.ss ·19z.3e
RER 365.7 274.4 166.5 375.5 491.9 750.3 1036.3 1450.3 2042.3 2801. 0 3903.0 5216.9 345.3 345.2 296.l
WLBH 199.8 198.9 zoo. 0 199.8 1•n.9 194.l 194.0 194.0 193.7 188.9 190.0 1115. 3 205~4 206.4 206.3
TOROUE o.o o.o o. 0 o.o o.o o.o o.o o.o o.o o.o o.o o .• o o.o o.o o.o I-'
HP o.oo o.oo o.oo o.oo 0.01 0.02 0.03 0.01 0.12 0.10 0.21 0.40 0.02 0.02 0 •. 02 v, N
TABLE.VIII
DATA FOR HEAT TRANSFER TES.TS WITH GULF HARMONY OIL 151 AND THE 4.039 INCH DIAMETER BLADE
DATE 07/04 07/04 07/04 07104 07/04 07/04 07/04 07/04 07/04 07/04 07/05 07/05 07/05 07/05 07/05 TIME 1300 1330 1400 1430 1500 1530 1600 1645 1715 1755 1100 1130 1200 1225 1255
TOI 127.70 128.99 131.64 133.50 135.71 163.41 157.52 164. 21 139.03 133.37 174.77 174.27 174.10 174.27 174.07
Tl 21 129.33 130.24 132.49 134.25 136. 18 165.42 158.73 165.89 139.36 133.74 175.81 175.11 174.84 174.98 174.57
Tl3l 130.48 131.26 133.2.0 135.10 137 .16 166.23 159.54 166..93 139.80 133 .54 175.'l5 175.28 175.11 175.28 1.74.74
Tl41 131.26 131. 84 133.06 134. 5'l 137.26 165.45 159.41 166.33 139. 26 133.94 175.51 175.14 174.81 -174.98 174.51
Tl 5) 131.23 130.99 131. 77 134.08 137.47 162.97 158. 19 164.08 139.23 133.16 173. 84 173.47 173. 27 173.40 174.47
Tl61 130.52 129.60 131.40 133.74 137.40 159.54 156.44 160.78 140.14 133 .33 170. 89 110.22 169.92 170.29 110.02
Tl7) 127.97 127.39 131.09 133.33 137.91 155.00 153.45 156.48 139.50 132.49 169.41 168.21 167. 77 168.37 168.37
Tl8l 126.27 126. 75. 130. 9'l 132.15 136.55 149.77 149.60 · 151.32. 138.82 131.98 165.12 164.41 165.19 166.02 l!>!,.43
Tl'll 124. 88 126.34 130.28 131.23 134.69 144. :;,o 145.01 145". 76 137. 20 131.30 161.19 161.76 163. 74 164.85 165.35
Tl 101 121.61 123.68 126.75 128. ll 131.47 137.67 139.67 13'l. 50 133.88 128. 5 B 157.49 l 5'l.54 162.20 163.67 164.3"5 ·
Tl 111 116. 70 118.92 122.12 123.72 126.95 131.81 135.16 133.94 129.46 124.16 152.67 155.70 159.07 160.45 161.32
TEJL 101.85 101.% 102.13 102.16 101.68 100.62 101.47 101.23 102.85 103.12 129.40 131.16 133.67 135.81 137. 60
TEI 102.'l3 103.17 103.41 103.65 103.2!) 101.25 102.58 101,93 104.20 104.47 132. 47 136.68 140.74 143.ll 145.68
TEO 114.91 114.22 113.71 113. 71 111. 2CJ 103.24 110. 63 104.30 116. 61 116.44 14(). 19 152. 7-0 c 152. 70 154.28 156. 30
TEOL 115.41 115.40 115.93 115.83 115. 42 113.50 114.69 113. 78 116.47 ll6.A8 148.09 150.11 151.80 153.41 155.37
TR A TIO 0.08 0.09 0.09 0.11 0.11 0.05 O.OA 0.06 0.10 0.10 0.16 0.29 0.39 0.41 0,45
OL 34.17 34.57 35.42 36.48 38.38 5'l.'H, 55.()7 60.67 39.81 36.03 68.39 68.07 67.78 67.93 67.53
0 1304.80 1304.40 1348.13 1336.43 1332.85 1320.19 1311.70 1312.24 1335.88 1337.96 3958.66 3988.40 3996.34 4029.84 3953.68
HC 30.51 29.49 32.85 30.54 25;.9() 10.62 12.79 10.42 27.47 32.37 60.79 67.20 74.61' 81.03 83.67
AGRPM 153. 38 116.09 78.80 5'l. 81 41.70 - 23.46 5. 73 H.43 40.71 77.45 332. 92 414.54 483.78 574.67 697.03
RER 238.4 18 l.O 124. 6 94.7 65.l 34.2 8.7 3·4. 7 65.8 126.6 1336. 2 1791. 9 2233.5 2183.5 3565.2
WLBH 207.3 207.3 206.3 206.3 204.4 212.6 206.4 216.9 . 206.2 205.2 412.0 407.5 411.0 402.7 398.4
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o f-'
HP 0.01 0.01 o.oo o.oo o.oo o.oo o.oo o.oo o.oo o.oo 0.03 0.05 ·0.07 O.H) 0.16 \J1 \..,J
TABLE VIII (Continued)
DATE 07/05 07/05 07/05 07/05 07/07 07/07 07/07 07/07 07/07 07/07 07/07 01101· 07/07 07107 07/07 TIME 1325. 1355 1420 1455 1045 1120 1210 1245 1320 1355 1425 1455 1530 1605 1640
Tfll 174.84 175. 75 177.45 178.96 127.39 128.21 131.16 134.96 140.14 153.18 162.33 165.42 163.44 157.32 157.15
T( 21 175.24 176. 18 177.52 179.29 128.61 128.95 132.35 135.84 140.99 155.97 163. 67 165.89 163.84 158.30 157.82
T(31 175.44 176.25 177.49 17'1.22 129.46 129.2'1 133.30 135.98 142.61 .157 .86 164.01 165.52 163. 61 158.53 158.19
H4l 175.24 175.98 177.15 178 .• 82 130. 92 130.52 134.38 136. 76 · 144.74 158.23 163.10 164.08 162.8.3 158.16 .· 157.69. ·
Tl5l 173.57 174.47 1 75 •. 64 177 .18 132.32 131.43 134.52 136.89 146.70 157.32 160.38 161. 05 160.2.5 156.68· 156.34
Tl.61 171.09 172.06 173.27 174.94 131. 91 130.69 134.05 137.26 147~38 154.q6 · 157.15 157. 62 156.98 154.69 154.49
Tl71 169 •. 61 170.f.2 171.93 173.60 129.46 129.09 133.57 136.45 146.53 15i.32 152.:84 153.31 153.28- 151.80 151.46
TISI 167.80 168. 74 169.92 1 71. 63 127.49 128.38 132.35 135.16 143.93 146.67 147.85. 148.25 148.69 147.85 147. 61
Tl9l 166 .• 70 167.57 168.78 170.49 126. 61 127.46 130. 79 133. 50 · 140.11 141.60 142.54 143.02 143.66 143.42 143.32
Tl 10 I . 165. 52 166.39 167.77 169.45 123.62 124.67 127.43 129~97 134.-42 .135.37 13.6. 38 137.03 i38.04 1.38.62 138.62
Tl 111 162.73 163.74 165.19 166.90 118.57 119.94. 122.94 125.35 1211.75 129.84 130.96 165.45 133.40 134.72 134.72
THL 139.26 139.77 139.80 140.ll 102.37 l 01. 61 101.58· 101.85 102.09 101.96 102.4.7 102.92 103.22 ·102.95 · 102.81
TEI 148.72 150. 71 153.34 155.59 103.17 102.48 102.62 103.06 102.93 102.76 102 .• 93 103.51 104.06 103.61 . 103.30
TEO 159,47 161.42 16_3.90 166.19 113.03 114.05 113.37 109.26 108.58 104.47 104. 37 105 •. 16 106.53 113.03 . 113.11
TEOL 158.19 160.21 162.57 164.88 114.09 113.15 llZ°.90 113.47 113.54 112.9q 113. 34 113. 70 114.53 114.25 114.12
TRAT_IO o. 50 o.53 0.59 0.63 0.01 0.08 0.09 0.10 0.07 0.01 0.04· 0.06 O.OT 0 .. 06 0.04
QL 68.16 68.79 69.80 71.25 33.q4 33.66 3&.,4 38.01 43. 81 54.14 58.04 58.83 57.82 54.08 53~71
Q 3qa2.44 3933.14 3960.82 3996.96 1350.30 133q.94 1352.39 1350.12 1·329.79 1321.14 1327.88 1325.41 1326.42 1330.16 1330.·53
HC 100.86 106.23 115.21 121 .• 63 29.36 28.66 25.46 25.29 17.65 12.03. U.54 U.67 11.12 13.40 13.68
A:GRPM 812.63 ·922.61 1014.26 1087.58 133. l7 97.23 59.92 47.81 37.70 3().27 23.Q6 16.28 9.21 · 5.24· lt,85
RER 4463.9 5320.0 6200. 0 7015. 2 201.s .143. l 87.9 71.4 56.3 44.5 34.3 24.6 14.2 a.o .,7.4.
WLBH 390.3 39q. a 382.2 378.l 247.8 · 247.;9 252.3 245.1 243.7 249.4 253.7 255.1 2'>3.5 245.0 245.0
TORQUE o.o o.o o.o -o.o o.o o.o o.o o.o . o.o o.o o.o o.o o.o o.o o,.o I-' v,
HP 0.23 0.31 o •. 37 0.43 0.01 o.oo o.oo o.oo 0,00 OoOO o.oo o.oo o.oo o.oo. o.oo. .i:--
TABLE VIII (Continued)
DATE 01101 07105 07/05 07_!05 07/07 07/07 07101 01101 07/01 01107 07107 01107 07 /07 07107 07/07 TIME 1715 1355 1420 1455 1045 1120 1210 1245 1320 1355 1425 1455 1530 1605 1640
Tl 11 128. 58 l 75. 75 177.45 178.96 127.39 128.21 131.16 134.96 140.14 153. 18 162.33 165.42 163.44 157.32 157.15
Tl21 128.07 176.18 177. 52 1 79. 29 l2R.6l 128.95 132.35 135. 84 140.99 155.97 163.67 165. 89 163. 84 158.30 157.82
Tl31 130. 14 l 76. 25 177. 49 179. 22 129.46 129.29 133.30 135.98 142. 61 157.86 164. 01 165. 52 163.61 158.53 158.19
'tt41 131.67 1 75. 98 177.15 l 78. 82 130.92 130.52 134.38 136.76 144.74 158. 2 3 163. 10 l-64.08 162.83 158.16 l'H.69
'tis> 132.72 174.47 175.64 l 77. 18 132.32 131.43 134. 5 2 136. 89 146.70 157.32 160. 38 161.05 160.25 156.68 156. 34
Tl61 133.13 1 72. 06 l 73. 27 174.94 131.91 130.69 134.0 5 137. 26 l47.3A 154. 96 157.15 1 57. 62 156.98 154.69 15.4. 49
Tl 71 132.01 170.62 l 11. 93 l 73. 60 129.46 129.0'l 13 3~ 57 136. 45 146.53 151.32 152.84 153. 31 153. 28 151.80 151.46
H81 130. 24 168.74 169. 92 1 n. 63 127.49 128.38 132.35 . 135.16 143.93 146.67 147.85 148.25 148.69 147.85 147.61
Tl9) 127. 05 167.57 168.78 170.49 126.61 127.46 no. 79 133. 50 140. ll 141. 60 l.42.54 143.02 143.66 143.42 143.32
T( 10 I 121.34 166.39 167.77 169.45 123.62 124.67 127.43 129.97 134.42 135 .37 136.38 137.03 138. 04 138.62 138. 62
Tl 111 lH,.15 163.74. 165.19 166.90 118.57 119.94 122.94 125. 35 128.75 129.84 130. 96 165.45 133. 40 134.12 134. 72
Tl:l l 104. 32 139.77 139.80 140. 11 102. 3 7 101.61 101.58 101.85 102.09 101. 96 102.47 l 02. 92 103.22 102.95 102.81
TEI 105.33 150. 71 153.34 155.59 103. 17 102.48 102.62 103.06 102.93 102. 76 102.93 103.51 104.06 103.61 103. 30
HO 116. 65 161.42 163.90 166.19 113.03 114.05 113.37 109. 26 l O 8. 5 B 104.47 104.37 105.16 106.53 113.03 113. 71
TEOL 116.91 160.21 162. 5 7 164. 8 8 114.09 113.15 112.90 113.47 113.54 112.99 113.34 113.70 114. 53 114. 25 114, 12
TRATrO 0.00 o.53 0.59 0.63 0.01 o.oa 0.09 0.10 0.07 0.07 0.04 0.06 0.01 0.06 0.04
Cl 34.45 68.79 69.80 11. 25 33.94 33.66 3,:,.34 38.01 43.81 54. 14 58.04 58.83 57.82 54.08 53. 7l
Q 1366.68 3933.14 3960.82 3996.96 1350.30 1339.94 1357..39 1350.72 1329.79 1321.14 1327.88 1325.41 1326.42 1330.16 1330.53
HC 34.24 10&.23 115.21 121.63 29. 36 28.66 25.46 25.29 17.65 12.03 11.. 54 '11.67 11.12 13.40 l}.M
AGRPM 249.20 922.61 }014.26 1087.58 133.17 97.23 59.92 47.81 37.70 30.27 23.06 16.28 9. 21 5.24 4.85
REP 412.0 5321).0 6200.0 7015.2 201. 8 11-3. l •n. 9 71.4 56. 3 . 44.5 34.3 24.6 14.2 B. 0 "l'.4
Wl8H 240. 5 389. B 382.2 378. l 247.8 247 •. 9 252.3 245.1 243.7 24<:J. 4 253 .1' 255.l 243.5 245.() 20ls5.0
TORQUE o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o o.o I-' \Ji
HP 0.03 0.31 o.:n 0.43 0.01 o.oo o.oo o.oo o.oo rloOO o.oo o.oo o.oo OoOO o.oo ,..,..,
TABLE IX
DATA.FOR HEAT TRANSFER TESTS WITH ETHYLENE GLYCOL AND THE 4~000 INCH DIAMETER BLADE
OATf. 07-09 07-()9 07.,-09 07-09 07-09 07-09 07-09 07-09 07-09 07-09 07,-12 07-12 07-12 07-12 .07.,-.12 TIME 1250 l 305 1332 · 1341, 1409 1420 1500 1517 1543 162 2 .· 1015 1035 1047 1124 · 1135
Tl 11 92.54 92 .54 93.0.8 96.74 94.91 91.26 90.58 90.i6 .-89.96 88.65 99.76 96.-70 93.47 91.9'3 91.20
Tl2J 93.26 93.2:i 99.42" 97._32 95.74 ···91.61 90.89 .· 90.47 90.27 101.13 lOL.06 · 96-~ 74 93.81 92.23 91.40
Tl 3 I 93.23 93.V:, 100~45 97.53 95. 64" 91.57 90.95 90.-51 88.58 101. 89 102.50 96.43 93.67. 92.19 91.37 ..
T14) 93.30 93.12 100.72 97.35 9_5. 57 91 •. 64 90.95 90.47 90.30 101.96 102.98 . 96;,·25: 93.64 92.09 91.30
TIS"! 92 .95 92.81 l 01. 41 97.39 95~39 91.47 90.78 90.27_ 90.16 102.33 102. 30. .95.88 93. 2(, 92.23 91.09
f.( 6) 92. 95. 92.99 loo. 96 97.32 95.50 91."51 90. 'Ta 90 .• 23 90.20 102.30. 101. 27 95. 84 · 93.23 91._78 90.99
Tl ll 92. 85 92.88_ 100.11- W:,.77 95.15 91.44 90. 71 90._20 90.13 101. 82 100.03 9·5·. 60 93.12 91.64 9!l. 89 •.
TIS) 92;s1 92~78 99.24 96.8.4 95.15 ~l.33 90.64 . 90 .13 ·90_.09 101.23 98.59 . 95. 53 92~1,l 91.47 90.82
Tl9l 92 .88 92.91 96.32· 96 .'70: 95.36 91.40 90.71 90.09 ·. 90.16 98.63 97.08 95.67 92 •. 81 91.44 90.78
Tl 10 I 92. ~4 . 92.44 94.50 "94.26 94. l 9 91~16 90.51 89. 92. 90.06 96 .. 2<;1 96.·98 94.67 92.47 9-1.23 90.61
rt 111 91.40 91.37 93.95 92. 81 92.H 90.33 89. 78 89.37 89.58 95.46 96.67 92.61 91.-44 90.40 89~96.
. Hll nu.~"'1 :)(J. 'l'.;. 8/,. 30 H6.33 86.30 86.54 860 5·0 86.64 87. l6 86.·99• .84 •. 85 . Rb-. 09 86.68 86.89 87.13
t:EI "87 .17 87.24 87.24 137. 13 87.07 87_.38 87 .4.8 · 8 7 .-51· ,, 88 •. 20 87.89 86.24 86.96 01. s1 · 87.76 88.17 ..
TEO .Btl.38 . 8-8.45 ; 98. 31 88.31 88.27 ·88.58 00.i.e 88.69 89.45 89.34 87. 69 88.51 89.03 89.24 89 •. 62
TEOL. 138.38 88.4_5 88.31 88.31 88.27 8!3.58 88 .• 62· 88.69 89.45 89.34 87 •. 69 88.51 89.03 89.24 89.62
T-R4Tl0 0.38 0~40 0.47 0.41 .o. 39 1).4•1 0-.44 0.4.3 - 0.46 0.3_8 0.49 0.36. 0~35 0.37 0.42·
Ql 10_.74 !0,'>5 14,S<i 12.99 il.9'l 9.85 9~48. 9.22 9.n 15.60 16.20 12.37 10.93 10.09 9.66
.Q 101,11..34 1A6<J.5B .1e41~n 1iin.3s 1a_61.09 1a-s2.02 1002.20 1913.69 1s99.2i-19;,.a.n 1948~39 i969.38-_t<Jso.11: 1971.66 1961.43
HC 187 .06 19.5.63 n.oo 100.54 126. 79 .. 286,46 36fl .• L9 ·471. 28 797.23 75.90 65.36· 126.02 203. 78 295.85 483.97
AGRPM 243.ill> 68.18 113.51- · 155.67 345.30 473.72 604~58 • 769.4"3 69.88 29.24 ·121._94· · 248 .•. 53;. 429.63. .. 641.96 ·z43. r,z
RH 10905.6 10911.fl 3047. 8 5070.4 F;94t'>.3 15510.3 21305.8 27224.0 3.5190.4 us4.o •1286.2· 5454.7 11243 .• 3 19527.l 2942·1~0
·wu,H 2574.8" 2'>65. i> 2';64.4 . 2570.4 256f,.() 2543. 5 2s1:i"8.s 2570 .1 2604~ 1 21n.a 2246,0" 2368.0 .22.49.5 2U8.9 2272. l
TORQUE o. 0 o. ()· . -o.o o. o· o.o o.o 'o. Q o.o o.o o.o o.o o.o -o.o o.o o.o I-' Vt
HP o.oo· ()., .J.J '.l.'J,l' 0.00 · 0.01 o.oo 0.06 -a.ob o.o.o o.oo o.oo o.oo o.oo -0.00 o.oo °'
TABLE IX (Continued)
DATE 07-,12 07-12 07-12 07-12 07-12 07-12 07-14 07-14 07-14 07-14 07-14 07-14 ,07-14 -07-14 . 0'1-14 TlME 1145 1220 1235 1315 1345 l 640 0855 0915 0937 1047 1226 1305 .. 1342 1355 1415
Tl 11 91 •. 13 96,67 92,23 131. 77 133 •. 88 122,05 116,19 110. 45 132.08 128.34 120.07 ll8. 23 106.31 132.32 131,67
T12l 91,23 97,66 92,64 135. 0.3 132,25 123,17 119,90 113,87 131.87 ·128. 68 121. 06 119.53 140.52 131.98 133.33 e
Tl31 91,23 97. 5'1 92,64 138,62 136, za li5 .o l 120.35 113.25 131.47 128,55 122.42 120,31 141.80 131.67 133.77
Tl4l 91,16 97,42 · 92,61 139.20 l 34. 86 123,34 119.36 110. oo 124,77 125,25 120.12 118,92 141.90. 131.16 133.03
Tl 51 90.92 97.,Jl 92,40 137,13 135,98 122,53 113. 18 111,88 117. 28 125,22 119.39 l.18,20 139. 97 132. ll 132,99
T(6) 90, 82 · 97,22 92,37 l 67, 33 138.45· 123,28 · 119,02 116,22. 136,05 129,23 119.26 1 t7, 89 143, 15 132.18 133.33
Tl7l 90,75 96,91 92.30 131,23 135.81 124,74 115,95 114, 17 135,81 129,02 HB,92 117. 45 133. 37 132,45 132,89
Tl.81 90,61 91-,. 9 1t 92.16 127,83 132,93 125,52 · 115,74 .113,.25 129~09 128,82 118, 54 116, 19 128,41 131,74 132.11
' Tl9) 90, 58 96.98 92 .• 13 124,57 128,34 126,51 115 •. 64 1.12,94 125. 73 128,72 118,M! 118,00 125.05 12(,. 85 127.29
T(lOl 90.44. 96.oc; 91, 95 124,57 123,14 124 .• 17 ll3,52 110~69 122,39 128. 58 117,21 116, 60 124.19 121.20 122.25
Till I 89,82 93. 95 91,i6 1?;3.82 120.96 i20.45 l 09, 39 108,81 128,31 128,48 113. 80 112,98 124 ,40 11 7. 89 120.55
TEil 87. ::io 87,33 87.? 8 97, O'l 100,55 100.99 97,59 97.94 98.;39 96.19 98,04 98,08 98,52 99.21 99,t.2 r
TEI tlB,38 88, 10 88.4 5 99,43 101,83 l 04 ,06 lOi,97 104,38. 104,;09 101, 04 99,46 99,32 100,18 100.32 100.83
TEO 89,79 89, 65 H'l,89 103.3.7 l 05, 5 3 106, 42 '18,12 97,74 91.41 102.38 103,65 102.62 102.55 106.87 1!>3.68
··-TEOL 89,79 89,'>5 89,89 10.3. 37 105,53 106.42 98,12 --,n-J1t_ 91.41 102.38 103.65 102.62 102,55 106,87 103.68
TRATIO 0,43 0,33 0.37 0,37 0,26 0,56 .8. 32 o.oo o.o·o o. 78 · 0,25 0.21 o.41 0,14 0.30.
Ql 9.59 13,J2 10,37 39~76 36.67 28,83 26,24 20,38 29.78 30,10 27.12 25,95 41. 72 34,10 35.39
0 1948.81 2010.43 1994,86 4854.54 4842.27 5437.66 5195,72 5126.25 4811.11 4875.38 4979,13 4767,73 4697.20 .4745.83 4710.34
HC 573,50 l?R,44 330. 20 ·.69. 59 80,51 162, 55 161. 06 231.16 99.,92 108,47 144,19 144,47 62.15 90. 78 Bl.58
AGRPM 779 .07 145. 9.1 4 34, 60 29,21. 68,30 ·150,74 263.li 428.77 642.47 775.74 148~06 151.06 2.9.21 73.03 68,06
RER 35844.2 6686,R 2C033,7 1735.2 4235.7 9595,8 14912,2 24258,l 33968,8 46.044.6 II82"(,9 8885,2 1726.8 4555.2 4098.8
WLBH 222 2., 9 26.6,. 6 2211.7 2340,l · 2339~5 · 2362,6 2056.9 2025.;0 1970,0. 20H..6 1638.3 ,186' .. 7 1899,3 1797.0 1773. 7.
TORQUE o.o o.o . o. 0 o.o o.o o.o o.o o~o o.o o.o o.o· o.·o o.o o.o o.o f-'.
0~00 o.oo Vl
HP 0,00 0,00 o.oo o.oo o.oo o.oo o.oo o.oo o.oo . o.oo. o.oo o.oo o.oo --J
TABLE. IX (Continued)
DATE; 07-14 ,07-14 07-14 07-14 07-14 07-15 07-15 07-15 . 07-15 07-15 07-15 07-15 07-14 07-14 07-14 ·TIME 1453 1503 1523 1545 1600 0845 .0910 0950 1020 1047 1103 1129 1342 1355 1415
Till 118.78 . 112.'14 110.28 lOR.23 l 07. 30 136.89 132.15 122.32. ];14. 79 111.13 108.57 108.98 106. 31 132.32 131.67
Tl 21 120.07 1.13. 93 110.65 lOR.57 107.99 131'.16 133 .• 67 123.14 115.10 110.52 109~29 109 •. 11 . 140. 52 131.98. 133.33
Tl3l 119.97 113. 11 110.04 107.81 107.44 139. 64 133.13 122.25 114.51 110.28 100;23 108.81 141.80 131.67 ·. 133. 77·
Tl41 119.60-, 113.,42 11ff.28 107;64 ·107.61. 143.76 131. 70 120.38 114.00 109.53 108.57. ·107.92 141.90 131.16 133.03
TISI 119.22 113.08 110.11 .101. 30 101.3,1 148.09 130.45 118.85 114. 11 108.94 107.10 107.47 139.97. 132.11 132.99
T16l 119.43. l i"3 .42 109.4,2 107~13 106. 82 147.58 129 • .84 118. 13 112.81 108.81 106.68 106.72' 143.15 132.18 133.33
Tl7l 117. 14 112.81 l 0·9.2 5 107. 13 1'06. 96 144.91 129.26 1.18.06 lU.41 108.09 107.23 106.45 133. 37 132.45 132·.09
Tl8l ,118.92 lil.99 lCH.46. 107.06 106;72 142.17 128. 21 118.10 111.99 107. 8 5 .106.55 106.10 128.41 131.74 132. ll
T(9l 119.67 113.56 1°09.25 l 07.27 l 07. 03 134.21 129.26 i i7.;72. 113.63 108. 33 106. 86 106. 34 125'. 05 . 126. 85 127. 29
Tl 10 l · 118.20 112 .06 109.35 Hl7.l6 106.89 i29.33 126.98 116~,.ij ,110 • .89. 107.3? 106.5.8 105~79 124.19 12.1.20 122.25
Tl 11 l 114. 62 109.90 107.95 •1.os. 7n 106.03 127.56 121. 51 114.14 1oa.94 ·106.17 106.48 105.01 124.40 117.89 120.55
TEil 99.3!! 98.73 99.11 98.66 99. 86 94.26 91.ao: . 97~84 97.80 97.49 98. 59. 98.52 98.52 99.21. 99.62
· TEI 99.87 99~67 100.11 · 100,22 100.87 97.12 98~!,4 99.39 98.91 99. 32 99.46 ·. 100.90 100.18 100.32 100.83
HO 106.59 102.82 103 •. 10 106. 73 103.75 102.48 : 104.09 fos.2& 103.82 103.10 104.68 1.04.57 102.;55 106.87 103.68
TEOI: 106. 59 102.82 103 .10 106.73 103.75 102.48 · 104.09 105.26. 103.82 103. l O 104.68 104.57 102.55 106 •. 87 103.68
TRATIO 0.07 0.23 0.25 0.19 · 0.26 o.35 0.13 0.21 0.18 0.33 0.14 0.39 o.41 0~14 o.3o
OL '26.39 22.4R 20.54 18.95 18.93 43.08 ' ·34 .48 26.90 22.84 20.09 19.51 19.12 41.72 34.10 35.39
0 4805.14 4795.27 4868.63 4853.48 4902.84· 4800.55 4658.37.4743.36 lt744.09 4778.65 4885.03 5020.07 4697.20 4745.83 4770.34 r-
HC 163.52 215.13 309.09 s10.':fr 531 • .82 54.92 83.51 149. 39· 204.96 330.47 502.09 584.94 62.15 90.78• 81.58 ·
AGRP'1 150~88 270.16 430. 78 ,' 643. 07 774. 71 34~93 72.93 155.-17 271.95 433.47 646.48 773~01 29. 21. 73.03 68.06
RER 9351.6 15968.9 25628.8 40017.5 46706.4 l 967.·6 434700 9431.4 16186.2 25646.6 39033.4 47084.7 1726.8 4555.2 . 4098.8
WLBH 1804. 6 l!:!26. 6 1737.0' 170R.4 1687.9 800 .'7 783.4 1044~0 U09.9 1324.9 1294.1 1220i5 1899.3 J197.0 ·· 1773.7
TOil.QUE o •. o o.o o.o o.o o.o o;o .o.·o .. o.o o.o o.o o.'o o.o o.o o.o o.o . f-'
HP o.OCJ o.oo o. 00 c. 00 o.oo o.oo o.oo o.oo o.oo ·o.oo o.oo o.o'o o.oo 0~00 v,
o.oo 00 ~
TABLE X
. DATA.FOR AGITATOR POWER REQUIREMENT TESTS WITH THE 3 .500 INCH DIAMETER BLADE
DATE NW XLA TW Tf T TEA VG VISW VISB HP QAGIT AGRPM RFR PN
03i29fl412 l 4.75 .79.'H 0.41 2.18 RO. 77 2499.62 2406 .• 66 0.00442 11.25 .128.0A 15.01 11.10
03/29114·14 l 8. 75 n.98 o. 55 4.17 81.0l 2497.03 7381.37 0.01397 35.57 211. 51 25.05 7.79
03/29/ 1416 l 5.75 A0.25 0.44 2.68 ,11.01 2461.94 2381.37 0.00615 15.67 144.83 17.16 10.69
03/29/1419 1 9.75 80.29 0.60 4.65 01.22 2458.20 2359.94 0.01769 45.02 23'l.BO 28.66 6.77
03/29/1420 l "· 75 R0.60 0.4<J 3.17 81.36 2424.92 2345.78. 0.00862 21.93 1 n. 51 20.62 9.01
03/29/ 14?1 1 10. 75 en. 74 0.65 5.13 lil. 53 2410.30 2328.22 0.02204 56.11 270.89 32. Bl 5.85
03/29/1423 l 7. 75 80.94 0.52 3.67 81.67 2388.56· 2314.2'l 0.01100 2 e.20 190.44 23.20 8.47 ,,
03/29/1425 l 11. 75 81.12 0.69 5. 62 81.84 2370.62 2297.01 0.02639 67.17 295.99 36.33 5. 37·,
03/29/1426 l 5.25 81.19 0.43 2.42 81,86. 2363.49 2295. 29 0.00535 13.61 139.14 17.09 10.48
03/29/1427 1 12.25 81.32 o. 70 5.88 :82. 15·· 2349.31 2 266 .30 0.02915 74 .• l'l 312.44 38 .• 86 s.05·
03/29/1429 l r,. 2.~ 81.50 0.47 2.91 82'.15 2331.72 2266. 30 0.00155 19.23 163.43 20.33 'l.14
03/29/1431 t 12.75 81. 88 o. 70 6.15 84.47 2293.57 .2052.36 0.03269 83.22 335. 29 45. 98 4.5'l·
rl3/ 29/ 1436 l 7.25 •H.46. 0.51 3.41 81.15 23Vi.B 2367.06 o.oo9<J2 25.25 183. 22 21. 8.3 8.51
03/29/1439 l 13~25 ~l.46 o. 70 6.41 81. 55. 2335.23 2326.48 0.03337 84.96 328.07 3'l.T6 4.99
03/2'l/1440 l ·0.2s 81.50 o. 55 3.'ll 81.74 2331.72 2307. 36 0.012118 32.78 207.90 25.41 '7.56
03/29/1441 l 13. 75 Sl.60 0.10 6.61! 82.22 2321. 24 2 259. 54 0.03686 93.83 347.<JO 43.·40 4.62
OV29/l442 1 9.25 81. 88 0.60 4.38 82.40 2293 .• 57 2242.74 o.oH,78 42.73 241. 56 30.36 6.29
03129/1445 l 14. 25 R2.05 0.10 6.95 83.00 227f,.48 21R5.12 0.04093 103.94 370.61 47~78 4.24
03/29/1446 l 10.25 R2.43 0.65 4. 86 8~.09 223'1.40 2177~04 0.02095 53.33 271.63 15.15 5.52
03/29/1448 l 14.75 82.67 o. 70 7. 21 113. 57 22lf>.1•8 2132.40 0.04541 · ll5.59 396.96 52.43 3.84.
Ol/29/14.49 l 11. 25 82.RR 0.70 5.35 83. 74 21%.51 2116. 73 o. 02612 66.48 307. 85 40.96 4.73
03/29/1450 1 15.25 113.19 O. TO 7.48 .1n.n 2H,7. 3R :no1.19 0.04799 122.16 .404. 57 . 54. 22 3.83
03129/145{ l 12.25 83. Tl 0.70 5 •. R8 84.57 ?119.!15 2 043. 36 · ·o. 0320.e 81.67 343.93 47.37 4.17
03/29/1454 . l 15. 75' <14.07 0.70 7.75 84. 75 20'9 l. 'l3 2028.46 0 •. 05399 137.43 439.52 '60.98 3.36
0312'l/ 1455 1 16. 75 84.40 o. 70 8.2R ai;. 25 ?058.l9 l'l85.98 0.06143 156.38 467.96 .66.29 3.17 ~
03/2'!/f456 l 17. 75 84.61 o. 70 A.Bl 85.61 2040.37 1955~87 0.07031) l 79.19 503.110 72;.45 2.91 v, --0
TABLE X (Contin·ued)
OATF NW lCLA TW TF. T TEA VG VISW VISB HP QAGIT AGRPM REA PN
03/29/1457 l 18. 75 84.99 0.10 9.34 85.75 2007~ 82 1944.55 0 .08371 213.10 565.01 Bl. 72 2.46
03/29/1459 l 19. 75 85.30 o. 70 9.88 85.99 1<181 .. 64 1924.92 0.08075 205.57 515.65 75. 33 3.12
03/29/1460 l 20. 75 85.78 o. 70 10.41 8'>.47 1941.73 1.886 • 36 0.09759 248.43 591.2'1 88.12 2.50
03/29/1501 l 21.75 86.lf. 0.70 10.94 ~6.89 1911.04 1854.05 0.10756 273.82 6i9.99 93.99 2.39
03/29/1502 2 14.00 ~8~54 o. 70 11.98 91.64 1731.24 1526.23 0.12344 314.23 649.65 ll'l.28 2.39
03/29/1503 2 15.75 87.23 0,70 H.55 !17. 83 1827.63 l 782.46 0.17638 449.00 821.06 129.39 l,69
03/29/1505 2 17,75 88_.13 0.10 15.33 88.37 1761.00 1743.57 D.20476 521.2'> 842.03 135.61 t. 82
03129/150t. 2 19. 75 119.02 0.70 17.12 89.30 1697.27 16'78.22 0.24267 617.74 !'193. 71 149.45 1.80
03/29/1507 2 21.75 90.09 0.70 18.91 89.97 1624.86 1632.85 0.30673 780.81 1022.82 175.72 l,'52
05/25/1620 l 5.75 f,3.17 0,28 2.84 62. 68 '5480.38 5615.8'1 O.OOZll 5. 3't, 46.70 2.37 107.89
05125/1622 l 7.75 <,3, 10 o. 32 3,R7 ,,~. 70 5499°0 50 5610.93 0.00425 lo. 81 · 69.18 3.52 66.93
05/25/1623 l 9. 75 63.07 o. 35 4,'10 62.79 5509.09 .5586,49 0.00694 1 7.66 89.23 4,56 50.95
05/25/1625 l 6.75 63,10 0.30 'I. 36 62. 72 5499.50 5606.03 0.00'104 7.73 57.05 2,90 85,41
05/25/1626 l R. 7'5 63.10 o. 33 4,39 62.96 5499. 50 5537.96 0,00550 13,99 78,99 4.07 58.19
O'i/21>/1628 l 11. 75 63.13 0.39 5~93 62,96 5489. 93 5537.96 0,01069 27.20 113. 71 5. 86 37,93
'05/25/1629 l 13. 75 6'1.13 0.43 6. 95 63.13 54!'19.93 543-q .93 0.01508 3·a. 3A 136. 75 7.10 .30. 77
05/25/1630 l 15.75 63.27 0.47 7,98 63.?7 5451.85 5451.flS 0,02042 51.98 161.42 8.44 25.34
05/25/1631 l 10. 75 63.41 0,37 5.42 63,41 5414.013 5414.08 0,00858 21.!!5 99.91 5.26 44.92
05/25/1632 1 12.75 63.52 0.41 6,43 63.52 '5385.95 53R5,95 0.01304 33.20 121.,n 6. 77 32.61
05/25/1634 l 14,75 63.52 0,46 ·7.46 63,62 5385.95. 5357.99 0.01809 46.06 152.98 11.14 26.39
05125/1635 l 16. 75 ·'>3. 59 o. 49 'l.48 63.90 5367.29 52114.25· 0.02365 60.21 175.80 9.48 22.73
05/25/1636 l 18. 75 (,3,80 0.54 9,50 64. 21 5311. 76 5202.69 0.03056 77.79 202.75 11.11 19.15
05/7.5/1637 l 20. 75, f,3. 97 0,58 10.53 64.67 5766,'lO 5087.45 0,03791 '16.51 227.07 12. 72 16.92
05/ 25/ 1639 l 17. 75 f,4.21 o.s2 F!.99 64.98 5202.69 500'1,41 0 .02726 6'9,40 191.20 10,87 20.38
05/ 25i 1640 l 19. 75 64.42 0~57 10.01 65,02 '5149,13 501)0,82 0.03512 89.41 221. 34 12.61 16.92 !-<
05/2'5/l.641 l 21.75 64,67 0,61. 11.. 03 65,50 5.087.45 4882.40 0.04276 108.84 244,40. 14 • .26 15. 31 a,. 0
TABLE X (Continued)
DATE NW XLA TW TF T TEA VG VISW VISl3 HP QAGIT AG RPM RE~ PN
05/25/1642 2 11. 75 65.05 o. 56 10.11 65. Fl9 4992.25 4791.64 0.03449 87. 80 215.11 12.78 10._12
05/25/ 1643 2 12.75 65.33 O. 6Z 10.95 66.27 4924.32 4 702.84 0.04325 110.10 249.10 15.0R 14.63
(15/ 25/lt,44 2 13. 75 65.68 0.66 11. 80 -66.56 4840.90 4635.53 0.05150 131.10 27"5.24 l-6.90 12.92
05/25il645 2 15. 75 65.89 0.10· 13.-55 67.28 4791.64 4477. 76 0.06983 177. 75 325.04 20.65 10.64
05/25/1646 2 11. 75 M.44 0.10 15.33 67.76 4663.11 4373.60 0.09070 230.<JO 372.99 24.25 9.15
05/25/1647 2 19.75 66.83 0.10 11.12 611.63 4577.07 4194.56 0.11654 296.65 429.18 29.08 7.72
05/25/1648 2 21 .• 75 67.76 o. 70 18.91 69. 54 4373.60 4017.35 0.14639 372.66 · 48R .• 16 34. 52 6.59
05/25/1649 3 15. 75 (:,8.81 0.10 18. 74 11.01 4159.78 3737.0l 0.15253 388.29 513.14 38.97 5.92
05/25/1651 3 17.75 70.20 0.10 21.11 72.f:>3 3893.38 347_3.70 0.20686 526.58 61.6.05 50.29 4.64"
05/25/1652 3 19.75 71. 31 -o. 70 n.60 74. 71 3694.56 3155. 71 o. 2!',702 679.72 713. 36 64.01 3.87
05/25/1654 3 21.75 73. 50 0.70 2b.03 76.116 3336.83 - ~-62~48 o. 34 783 885.43 .842.53 83.24 3.06
05/25./1655 23 11.1,; 75~82 0.10 25~01 !10. 98 3000.16 2"31;!4.96 0.34963 890-,02 881,47 104.26 2.69
0.5/25./ 1656 :>3 12,75 78,66 0.70 27.12 83.19 2641.08 2167.38 0.46073 1172.8"5 - 1071.27 139.·24 1.98
06/05/1600 1 4.75 12.00 o.1a 1. 81 73.81 3445.80 3289.12 0.00206 5.24 71. 77 6.18 29.25"
06/05/1601 1 0. 75 72,84 -1. 13 3.59 T~.76 3440. 26 3297.01 0.00784 19.96 137. 82 11.84 15. 7.r,
06/05/1602 l 6. 75 73,01 o. 96 2.10 73. 72 3412.6fl 3302.29 0.00448 11.42 104.79 8.99 20.48
06/05/1605 l 10. 75 73.18 1.19 4.59 73.81 3385.36 3289.12 0.01211 32.51 175.33 15.10 12.45
06/0511606 l 12.75 73.29 1.19 c;.66 74.02 - 3369.09 H57.75 0.01888 48.06 210. 38 18.29 10.65
06/05/1607 1 16.75 73.53 1.19 7.79 74.29 3331.49 1216.48 0.03448 87.?6 279.14 24.58 B.33
06105/1608 1 14. 75 73.64 1.19 6-. 72 74.57 3315.52 3175.82 0.02668 67.93 250.26 22. 32" 8.95
06/05/1610 l 18. 75 73.98 1. l<J 8,85 74.99. 32',2. 95 3115.-9'5 0.04480 114.05 319.12 29.00 7.25
06/05/1"61 l 1 22.00 74.22 1.19 10.58 75.27 - 3226,74 3076. 78 0.06427 1-63.60 - 382.92 35.23 6.02
06/05/1612 l 20,75 74.75 1. 19 9.92 76.10 3150.71 2_962. 70 0.05846 148.82 371.70 35.50 _5.99
....... er-.......
TABLE XI
DATA.FOR AGITATOR POWER REQUIREMENT TESTS WITH THE 3.831.INCH DIAMETER BLADE DATE NW XLA TW TF T TEA VG VISW VJSB ·HP QAGIT AGIIPM R·ER PN
05/lt./.1420 l 6.75 ·e,5.11 0.65 3.01 63.80 4832.65. 5311.76 0.00222 .5.65 46.57 2 •. 50. 114. 79
05/16/1421 l 10.75 32.37 0.42 5.36 63.95 30856.36 5270.55 0 .00624 15. 88 73.36 4.75 57.50
05/16/1424 l 8.75 65.12 o.39 4.33 64.15 4975.17 5220.69 0-00402 10.23 58.51 .3.83 73.04
05/16/.1426 l 14. 75. f,4.98 0.50 7.41 64.48 5009.41 5135.84 0.01259 32.04 107.05 1.12 · 37.34
05116/1427 l 12.75 32.37 0.45 6.39 64.60 30856.36 5104 .. 99 0.00895 . 22.78 118.26 5.90 47.38
05/16/1429 1 18. 75 _65. 05 0.60 9.44 64.91 4992.25 5026.63 0.02264 57.64 151.21 10.21 23.84
. 05/16/1430 1 16. 75 f,5.29 0.54 8.44 6<;. 12 4932.75 4975 .17 0.01645 41.88 122.88 8.43 32.28
05/16/1432 1 22.15 65.61 0.64 H.21 65.5-0 4857.45 4882.40 0.02978 75.82 167.47 11.10 23.09
05116/1433 l 20.75 !>5.6S o. 62 10.·49 65 •. 85 4840.90 4799.81 o·.02623 66.76 157.-63 11.20 24.39
05/ 16/143,5. 2 i;>.75 .H.37 o. 63 10.93 6f,. 37 3085(,. 36 4678.96 0.02836 · 72.18 163.51 11.92. 23.63
05/11,/1437 2 16. 75 t,6.44 o. 77 14.37 6f,.84 4663. U 4573.20 o.oc;o67 l 2R.~R 222.27 16._57 16.82
05/16/ 1438 7 14. 75 37.. 37 {). 71 . 12.64 67.21 30856.36 4492.137 0.04010 · 102.oe 200.08 15.18 18.25
05/16/1':";0 2 2D.75 t,7.42 o. 91 17. Bl 68.10 4447. 71 4304.53 0.08032 204.46 284.44 22.51 12 • .73
.05/ 16/ I 44 l 2 18. 75 32. 37 o. 87 1·6.06 6!1 • .63 30856.36 '+:J.94.56 0.06796 172.99 266.84 21.66 13.05
05/16/1443 3 14.65 32. 37 o. 94 11.11 69 •. 61 30856.36 4004.09 0 .• 09000 205.88 297.04 25. 25 · 11.27
05/16/1444 3 16.75 32.37 1. 06 19.59 7().37 30851,.36 1861.50 0.10904 277.58 350.90 30.91 9.22
()5/16/1445 3 lA.75 70.2'3 1. 1 R 21.91 71. 76 3886.98 3617.19 0.14446 .367. 73 fol 5. 78 39.07 7.;35
05/ 16/ 1446 3 20. 7'5 32.37 l. 111 24 .• 34 73. lR 30856. 36 3385.36 0.17964 457.31 465 .• 45 4&.69 6.52
05/ 16/1449 23 11. 75 74.19 1.18 24.53 75._92 3-231.8!1 7-986.05 o_. l'l968 508.32 513.29 58.28 5.41
05/ 16/1450 23 13. 75 32.37 1.18 2R. 75 78.31 30!!'56.36 26!12.04 0.28336 721.34 . 621.53· 78.45 .4.33
05/16/l45f 23 15.75 32. 37 · 1.18 32. 97 80.94 30R56.36 2388.56 0.38444 978.64 735.36 104.05 3.55
05/ 16/1452 23 I 7~ 75 '12.37 1. l'l 37.18 83. 71 30856.36 2119.'35 0.5?.Q04 1346. 72 897~16 142. 79 . 2.70
05/ 16/1645 l 7. 75- 71.97 0.39 3.RO 6&.48 35132.13 46~5. 21 0.00366 9.32· f..0~11.4 4.46 59~24
O"i/16/1647 l 9.75 70.89 0.4'1 4.82 66.8R 3767.69 lt565.411 0.{)0605 15.41 79.21- 5.91 44.37
05/ lf-/1648 l 11. 75 70. 31t -0.4R 5.84 67. ;[>~ 3867.86 4477. 76 0.00910 23~17 98.~2 7.48 34.91 I-'
05/16/1649 1 13. 75 32.·37 o. 52 6086 67.52 30856.36 4425. 32 0.01282 32. 63 117. 88 9.08 28~53 a-. I\)
TABLE XI (C-ontinued)
DATE NW XLII. TW TF T TF.AVG VISW VISS HP IJAGIT AGRPH RFR PN
05/H,/1651 l 15.75 32.37 0.57 7.88 67.A(l 30856.36 4366.27 0.01716 43.68 137. 37 10.72 24.14
05/16/1652 l 17. 75 69.57 o. bl 8.90 613.20 4010. 72 4282.99 0.02188 5'5.70 155.03 12.33 21.1t2
05/ 16/ 1653 l 19. 75 32.37 0.65 9.92 6Fl.63 30856.36 4194.56 0.132746 6'l~89 174.53 14.17 18.84
05116/ 16'55 l 21. 75 32.37 o. 72 10.92 69.19 30R56.36 4084.46 0.03538 90.06 204.38 17.03 15.13
05/16/1658 23 9.75 70~20 l. Ofl 20.41 70.41 3893.313 3855.17 o. 11587 294.97 357.93 31.58 9.23
05/16/1660 23 11. 75 32.37 1. 18 24.53 71.87 30856.36 3599~61 0.11121 435.98 440.24 4t.57 7.34
05/ 16/ 1701 23 13.75 32.37 1.18 28. 75 73.53 30856.36 3331.49 0.24612 626.52 539.84 55.02 s. 72
05/16/1702 · 23 15.75 74.02 1.18 32.97 76.10 3257. 75 2962. 70 0.33698 857.81 644.57 n.1s 4.61
05/16/1703 23 17. 75 32.37 1. 18 3 7. 18 80 •. 75 30856~ 36 2461.94 0.50107 1275.52 84-9.74 116. 70 3.00
f-'
$
TABLE XII
DATA FOR A-GITATOR POWER REQUIREMENT TESTS WITH THE 4.000 INCH DIAMETER BLADE
DATE NW XLA TW TF T TE AVG VISW VISB HP QAGIT AGRPM RER PN
02/15/1600 l 4. 75 7q.35 0.38 2.21 79.92 2561.16 l497. 72 0.00191 4.86 54.43 7.37 43.51
02/15/1610 1 6.75 80.46 0.41 3.25 81.13 243q.65 2 368 .84 0.00390 9.93 75.79 11.79 27.72
02115/1615 l s.75 81.64 o. 50 4.22 82.17 2317. 76 2264.61 'O .006u3 16.87 98.95 16.09 21.11
02115/1620 l 10. 75 82.19 o. 57 5. 21 82.64 2262.91 2219.48 0.00987 25.11 119.41 19.80 17.94
02/15/1623 1 12. 75 83.09 0.66 6.18 83.17 2177.04 2168.99 0.01405 35.76 143.26 24.30 14.80
02115/1626 1 14. 75 83.74 0.77 7.15 83. 73 2116. 73 2118.29 0.01924 48.9q 169.77 29.48 12.19
02/15/1630 l 16.75 84.37 0.84 8.14 84. 23 2061. 41 2073. 56 0.02449 62.35 189.8 l 33.66 11.10
02/ 15/1632 l 18.75 84. 78 0.94 9.10 84. 78 2025. 50 2025.50 0.03110 79.11, 215.37 39.08 9.65
021 l 5/ 1635 1 20.75 85.64 1.03 10. 07 - 85. 38 1q53.03 1974.44 0.03844 97.85 240.63 44.78 8.56
02/15/1640 l 22.25 116.44 1.01- 10.84 -86. 23 18M.09 1905.53 0.04428 112. 71 257.64, 49.65 8.03
02115/2010 1 5.75 18. 83 0.34 2.78 79.04 2620.88 2596.88 0'.00257 ,, 6.54 58.26 8.28 40.13
02/15/2013 l 1. 75 1q.oa 0.46 3. 73 79.58 2592.90 2536._06 0.00525 13.37 88.80 12.91 23.18
02115/2016 l 9. 75 7q.10 o. 50 4.75 79.99 2522.57 2490.14 0.00759 1 q.33 100.85 14.93 22.88
02/15/2019 l 11.75 79.91 0.58 5. 73 80. 22 2499.62 2465.68 0.01111 28.29 122.28 18.28 18.79
02/15/2024 l 15.75 81.29 0.76 7.69 Bl. 19 2352.85 2363.49 0.02039 51.89 167.15 26.05 13.50
02115/2027 1 17.75 81.98 o. 85 !!.66 in. 67 2283.30 2314.29 0.02628 66.91 191.30 30.44 - 11 .• 62
02115/2029 l 19. 75 82.36 -0.92 9.65 82.22 2246.09 2259.54 0.03242 82.52 211. 82 34. 51 10.56
02/15/2031 l 21. 75 83.19 1. 01 10.63 82. 72 2167.38 2211.24 0.03947 100.47 234.12 38.97 9.52
02/ 15/20_34 2 14.75 83. 7l 1.-07 12. 28 83.36 211'}.!15 2151. 40 o. 04887 124-42 250.92 42.91 9.58
02/15/2036 2 16.75 84.37 1. 07 14~07 83.81 2061.41 2110.49 0.06449 164.17 289.02 50.37 8.28
02/l'i/2039 2 18.75 84. 78 1. 07 15. 86 84.33 2025. 50 2064.44 0.07286 185.48 289.73 51.60 9.29
02/15/2041 2 20. 75 85.64 1.01 17.65 84.87 0 1953.03 2010.11 0.10087 256. 79 360.47 65.65 6.68
02/ 15/2044 23 8. 75 ~6.82 1.01 18.32 85.78 1859 • 39 1941.73 0.10121 272.90 369.10 69.83 6.61
02/ 15/2048 23 10.75 89.20 1.07 22.53 87.0l 1eB5.H 1844.75 0.169811 432.45 475.41 94.60 .... 91 -
02/15/2051 23 12. 75 - 90.64 1. 07 26. 75 sq.04 1588.93 1767.29 0.23145 589.19 545.60 !_13.25 4.43 I-'
02115/20'54 23 14.75 93. 71 1.07 30. 97 !19.61 '1405.69 1657 .10 0•31346 797.94 638.,28 141.1-6 !. 75 CT'-.i:--
TABLE XII (Continued)
DAH NW XLA TW TF T TEA VG VI SW VISfl HP QAGTT AGRP~ RER PN
02/15/2059 23 16.75 96.15 1. 07 35.18 92. 85 1277. 56 1454.48 o. 41316 1051. 74 740.46 186.19 3.17
02/15/2122 23 16. 75 108.81 1. 07 35.18 107.37 800.70 842 .42 o.s2011 1324.14 932.23 401.08 2.02
02/20/1022 1 5. 75 12. 32 0.23 2.89 72. 30 3524.57 3527.4 3 0.0-0136 3.45 29.62 3.11 160.72
02/20/1029 1 4.75 12. 32 0.22 2.37 n.4o 3524.57 3510.35 0.00099 2.52 26.34 2.78 166.57
02/ 20/1032 1 5.25 12. 35 0.23 2.-63 72.46 3518.88 3501.85 0.00120 3.06 28.85 3.05 153.95
02/20/1036 l 6.25 72.49 o. 26 3.13 72.47 34%.20 3499.03 0.00178 4.53 35.84 3.79 118.95
02/20/1042 t 6.713 72.66 0.21 3.38 12 .68 3468.10 3465.30 0.00213 5.42 3<;).67 4.24 104. 91
02/20/1050 l 7.30 12.11 0.28 3.66 72.68 3451.36 3465.30 0.0024-8 6. 32 42.75 4.57 97.84
02/20/1054 l 7.75 72. 80 0.30 3.89 72.87 3445.80 3434.72 0.00292 7.45 47.46 5.12 .84.21
02/20/ 1056 1 9.25 72.94 o. 34 4.64 73.05 3423.68 3407.19 0.00432 10.99 58.65 6.37 65.116
02/20/1059 l 8.25 72.98 0.30 4.15 73.03 3418.17 3409.93 0.00320 8.14 48.60 5.28 85.71
02/20/ 1102 l 9. 75 73.08 0.36 4.90 73.10 3401.72 3398.99 0.00480 12.23 61. 86 6.74 62.45
02/2011105 l 8.75 7'1.15 0.32 4.40 73.17 3390. 'lO 3388. 08 0.00364 9.28 52.23 5. 71 78.76
02/20/1108 l 11. 25 73. 2Q 0.40 5.t<,5 73. 12. 3369.09 3363.69 0.00662 16.1!6 73. 91 8.13 50.49
02/2011110 l 10.25 73.39 0.16 5.16 73.50 B52.92 1336.83 0.00518 13.19 63.37 7.03 62.69
02120/1113 1 12.25 73. 53 0.43 6.16 n.53 3331.49 3331.49 o. 01) 785 19.98 80.311 8.93 46.53
02/20/ l ll 5 l 12.25 73. 57 0.43 6.15 13. 67 3321>.1·6 3310.22 0.00789 20.09 80.R6 9.04 45.-97
02/20/1118 I 13.25 73.~ 1 0.46 6.66 73.Al 3289.12 3289.12 0.00938 23.88 88.86 10.00 4!.17
02/20/1120 l 11. 75 73.91 0.41 ,;.n 73.96 3273.3Q 1265.56 0.00110 lA.06 75. 73 fl.58 50.31
02/20/1122 l 14. 75 74.09 0.51 7.41 74.09 3247.37 3247.37 0.01195 30.41 101.11 11.59 34.98
02/20/1124 1 13. 75 74.22 0.47 "· 91 74.22 3226.74 3226. 74 o. 01013 25.80 92.48 10.60 39.46
02/20/1126 1 15.25 74.40 o. 53 7.65 74.42 3201.16 3t9B.6l 0.01303 33.16 107.35 12.42 32.44
02/70/ 1128 1 14. 75 74.50 0.49 7.16 74.50 3185.97 3185. 92 -0.01094 27.85 96.32 11.18 37. 71
02/ 20/ ll 30 l 16.75 74. 85 o. 58 · 'l.40 71,. 83 Jn5.76 3131!.24 0.01607 40 .• 90 120. 63 14.22 28.21
02/2011131 1 15. 75 75.02 0.54 7.91 75. 02 3111.,n 3ll 1.02 0.01380 35.13 110. 06 13.08 'Jl. Ql f-'
02/ 2011 i. 33 l 17.25 75.33 O. M) 13. 65 75.21 3067.011 3084 .os 0.01122 43.85 125. 61 15.0b 26.79 °' \J1
TABLE. XII (Gontim.ied)
DATE NW XLA TW TF T TE AVG VISW V[Sl'I HP OAGIT AGRPM RER PN
02/20/113.5· l lS.25 75.58 0.62 9,15 75. 53 3033.40 3040.58 0.01919 48.86 .. 132.20 16.07 .25.61
02/20/1137 i · 16.25 75_.92 0.57 8 .• 14 75.6b 2986.05 302 i .4!1 0.01520 38. 70 · 117.69 14.40 28.75
02/.20/1139 1 17. 75 76.06 0.63 .11. 88 75.92 2967.35 2986.05 0.01874 47.70 13.3.00 16.46 24.56
02/20/1141 l 19.15 76.41 0.69 9 .• 88 76.20 292-1.21 2'14'3.79 0.02354 59.93 i51'.'.18 18.82 .. 21 •. 43
02/20/1143 l 18.15 76.69 0.6(, 9. 38 76.58 2884.90 2898.45 0.02124 54.06 142.75 18.20 · 22.52
02/20/ 1145 l 20.25 76.96 0.12 10.12 76. 82 2849. 13 2866.95 0.02537. 64.58 158.05 20.36 19.82'
02120/ 1146 1 19.2'5 77.28 o •. 67 9.64 11.01 28-09. 50 2 835 oll4 0.02224 56.61 145.53 18.95 22.26
02/20/1147 l 21.25 77.55 0.76 10. 61 77.47 2774.82 2785 .61 0.02852 7?.59 169.49 22.47 18.08
02/20/1149 ·1 22. 2.5 111. 00 0.82 11. 09 77. 79 2719 .• 55 2744.90 0.03224 R2.06 183.30 24.65 16.16
02/20/1151 1 20.75 78. 42 0.76 . 10.35 7!1.18 2669';,.67 · 2698.63 0002755 70.14 .167.88 22.96 17.98
02/20/1152 l 21~75. 7'1.73 0.80 10. 84 7.8. 52 263;2°.98 '2657 • 3fl 0,03090 78.66 179.79 24.97 16.42
03/17/1708 l 4.75 68.50 0.19 2.39 68.46 4222. 62 4229.67 0.00075 1.90 19.65 1. 72 301. 94
03/17/1712 l 9.75 68 •. 46 o. 31 4.94 - 6'1. 50 427.9.&7 · 4222.62 0.00391 9.95 49.89 4.39 96.64_
03/17/1714 1· 6.75 bR.50 0,24 3.41 68.50 4222.62 4222.62 0.00173 4.40 -31.91 2.81. 163.16
03/17/1717 1 11.75 68.53 o. 36 5,96 6g.50 4215.58 4222 .{,2 0.00586 14. 92- 61.99 5.45 75.51
03/17 / 1720 . 1 7.75 68.f,3 o. 26 3.92 6'J. 63 4194.56 4194.56' 0.00236 6.02 38.00 3.36 132.24
03/17/1722 1 12.75 6'3.67 0.38 6.47 68.88 4187.57 4145.96 0.00707 17.99 68.92 6.17 66.28
03/17/1725 l R.75 6'1098 0.29 4.43 69.05 4125.34 4111.66 0.00308 :i.85 43.86 3.96 H2.18
03/17/1727 1 5. 75 69 •. 02 0.22 2_.90 69.07 '411R.49 4108.2'• 0.00125 3.18 27.15 2.45 191.47
03/17/1734 1 13. 75 69.16 o. 41 6.97 69.33 4091.24 4057.46 0.00833 .21.20 75.29 6.89 .. 59.93
03/17 /1735 1 5.25 ,69.19 0.21 2.65 69.36 40A4.45 40':iO. 14 0.00099 2.51 23.53 2.1.6 232.76
03/17/1737 1 14. 75 -69.36 o. 43 7.48 69.-64 4050.74 3997.411 0.00980 24.95 . 82.62 7.67 · 53.37
03/17/1739 1 6.25 69.47 0.24 3.15 69.68 4030.67 -1990.88 0.00152 3._88 30.47 2.03 165.40
03/17/1140 .1 15. 75 69. 50 0.46 7.91.1 69.71 ·-4024.01 3984.29 0.01142 29.07 9_0.22 8.40 47~78
03/17/ 1742 1 1.2c; 69.64 0.25 3.67 . • 69._80 3997.48 3967.117 0.00205 5.21 35.21 3.29 144.11 I-'
03/17/1744 l 16. 75 59.68 0.49 .A.49 6'9.89 3.9'->0.'I!! 3951.54_ 0.01312 33.41 97.50 -9.15 43.50 °' O'
TA"BLE XII (Continued)
DATE NW XLA TW TF 'r Tf'AVG VISW VISB HP QAGIT AGRPM RER PN
03/17/1745 1 8.25 o'l.68 o. 29 4.16 69.99 3990.Sfl 3932.04 0.00291 7.42 44.13 4.16 104.21
03/17/1749 l 9.25 70.23 o. 33 4.65 70.34 3R86.98 3867.86 0.00413 10.51 55.95 5.36 72.43
03/17/1752 l l 7. 75 70. 30 -0. 52 8.99 70.51 3874.22 3836 •. 22 0.01497 38.12 105.01 10.1.5 39.74
03/ 1 711754 l 10, 25 70.55 o. 34' 5.18 70.58 3829.93 3823.6'> 0.00478 12.16 58.19 5.64 74.51
03/ 17 / 1756 l 18,75 70.62 o. 55 9.49 70.68 3817.39 3804.89 0.01718 43. 73 114.16 11.12 35.49
03/17/ 1757 l 11.25 70,89 0.38 5.67 70. 89 3767,69 n67,69 0.00623 15.85 69.27 6.82 -S7. 56
03/17/1759 l 19, 75 71.07 0,59 9.99 71,07 3737,01 3737,01 0,01939 49.36 122,39 12.14 32.52
OJ/17/1800 l 12.25 11.10 0,40 6,19 11.10 3730,91 3730.91 0.00714 18.16 72.74 7,23 57.00
03/17 /1802 1 20, 75 71. 31 o. 62 10.49 71, 38 3694,56 161!2,53 0.02180 55,50 131,06 13.19 29,78
03/17/1805 1 13,25 71,45 0,41 6.69 71,55 3670,55 3652,66 0 ,008 53 21.12 80,44 8,16 50,41
03/17/1806 l 21,75 71, 73 o. 65 10,99 71. 73 3623,08 3623,08 0,02421 61.63 138 ,-89 14,21 27.79
03/17/1807 l 14,25 71,87 0.45 7,19 71,87 3599.61 3599.6,l 0,01005 25.58 88,09 9.07 45,21 ·,
03/17/1809 1 22.25 72, l 1 o. 67 11,24 72, ll 3558,98 3558,'lfl 0,-02560 65.17 143.62 14,95 26.59
03/17/1811 1 20,25 72,28 0,62 10.22 72, 32' 3530,28 3524,57 0,02121 53,99 130.81 13. 75 29,15
03/17/1813 2 12. 71 72,66 o. 64 10,89 72.70 346fl.10 3462,51 o.o;n52 59,89 136. 21 14,57 28.65
03/ l 7/ 1815 2 13, 75 72,98 0,69 11. 77 72, 98 34l8, l 7 341 R, 17 0 ,02786 70.93 149,27 16, l 7 25.79
03/ 17 / lR 16 2 16. 7r; 73.36 0.83 14. 31 73. 36 3358.30 3358.30 0.04232 107. 74 186.48 20.56 Z0,09
03/17/1817 2 14. 75 73. 74 o. 75 12,60 73. 67 32q9.65 n10.22 0.03302 84.05 165.18 18.47 22.56
03/17/1819 2 1 7. 75 74.05 o. 91) 15.14 74,12 3252.56 3242.20 o.04qo9 124. 9,; 204.48 23,34 11.68
03/l7/lfl20 2 19.75 74.75 1. 01 16. 81 74. 75 315:), 71 3150. 71 0.06271 15 9. 63 235.25 27.62 14.84
03/17/1821 2 l '5. 75 75.06 o. 84 13.41 75.06 3106.10 311)6.10 0,04006 10l.9R 188.38 22.43 18.47
03/ 17 / 1822 2 20.75 75.61 1.01 17,65 7'5.61 302£.63 3028.63 0.07142 181,Rl 255.23 31,15 1.3.24
03/17/1824 2 21.75 76,A6 1.07 11'1. 54 76. 76 21162.4~ 2 875. 91 O. -OR 134 207.05 276.64 35.53 11.85
03/17/1825 3 16. 7'5 78.00 1.07 19,59 TR~OO 2719.55 2719.55 0.09548 243.05 307.34 4i. 72 10.15
03/l 7 /1826 3 .· 11. 75 78.69 1,07 20.eo 7A.38 2637.03 2673.79 0.10674 27 l. 72 323.54 44.65 9.73 f-l
03/17/1827 3 18.75 79. 73 1. 07 22.02 7~.14 2518.73 ~584.97 0.14020. 356.89 401·,'H •n.29 6.69 0--...;J
DATE NW XLA TW TF
03/17/1829 3 19.75 80.94 1.07
03/17/1829 3 19.75 RO. 94 l.07
03/17/1830 3 20.75 B2. 53 1.07
03/17/1831 3 21.75 83.88 1.07
TABLE XII (Continued)
T TEAVG VISW VISB H~ QAGIT AGRP~
?1. 23 RD.32 2388.56 2454.48 0.14210 361.73 385.68
23.23 8i,39 238A.56 2447.05 0,14210 361,73 385,6~
24.45 81.53 2229.42 232R,22 0.16102 409.90 415,32
25.66 81.26 2104.28 2160.97 0.18319 466.34 450.14
RER
57.92
58.09
65. 70
76.64
PN
7.66
7.66
6,96
6.22
I-'
°' a+
TABLE XIII
DATA FOR AGITATOR POWER REQUIREMENT TESTS WITH THE 4.-039 INCH DIAMETER BLADE DATE NW XLA TW TF T TEA VG VISW VISB HP QAGIT AGRPM RfR PN
06/22/ 1013 l 4.75 72.49 0.19 ?.40 72.49 34%.20 3496.20 0.00073 1.1!5 19.14 2.03 319.26
06/22/1016 l 8.75 72.66 0.25 4.47 12. 68 34M.l') 3465.30 0.00264 6. 7l 37.23 4.06 151.25
06/22/1018 l 6.75 72.63 0.21 3.44 72.65 3473.70 3470.89 o. 00148 3~76 27.03 2.94 . 221.19
06/22/ 1020 l 14.75 72. 63 0.3R 7.54 72. 63 3473.70 1473.70 0.00804 20.46 67.25 7.31 78.24
06/22/1021 l 12.75 72. 70 0.33 6.51 72. 72 3462 .51 3459_. 72 0.00590 15.02 57.11 6~23 93.76
06/22/ 1023 l lo. 75 72. RO o. 30 5.49 72.80 3445.8-0 3445.80 0.00415 10. 57 47.69 5.23 113.28
06/22/ 1025 l 18.75 72.91 0.45 9.59 72.91 3429.19 3429.19 0 • .01292 32.89 84.93 9.35 62.46
06/22/1026 1 16.75 72.98 .o. 41 8.57 72.98 3418 .1 7 3418.17 0.01034 26.32 u,. n B.41 r,9.41
06/22/1028 1 2"2.05 73.15 o. 56 11. 24 73.15 3390.80 H90.80 0.02016 51.32 113.15 12. 6-0 41.21
06/22/1030 1 20:15 73.43 0.49 10.62 73.43 3347.54 "3347.54 0.011'0_6 40.1!8 95.38 10.75 54.Bl
06/22/1031 2 12.75 n.c;1 o. 50 11.06 73. 53 3326.l6 3331.49 0.01723 43.86 9A.23 ll.13 53.85
06/22/1032 2 16. 75 73.81 0.64 14.50 H.81 3289.12 3289.12 0.03041 77.42 132. 27 15 .17 38.93
06/22/ 1033 2 14.75 73.95 o.5B 12.11 73.95 326!1.17 1266.17 0.02364 60.17 116. 68 n.47 44.0R
06/22/1034 2 21.75 74.36 0.82 18.79 74. 36 3206.25 3206.25 0.05232 133.lA 175.57 20. 66. 28.65
06/22/1036 2 19.75 74.64 0.11 17.05 74.64 3165.75 3165.75 0.04423 112. 59 163.57 19.49 29.96
Of>/ 22/1038 3 15.75 75. 33 O.A5 1q.60 75. 23 3067.01! 1081.65 o. 05 369 136.67 1A2.04 22.21 26.39
06/22/1039 3 l!I. 75 75.75 1. 01 22.08 75.61 3009.62 3028.63 o. 07753 197.36 221.40 27.55 21.18
0_6/ 2 211040 3 21.75 76.30 1. OB 25.65 76.10 2934.96 2962. 70 0.10641 270.89 261.58 33.27 17. 64_
06/22/104 l 23 13.75 77.14 1. O!I 2!1.f'5 77.14 2827 .03 2827.03 0.13723 349. 34 299.96 39.95 15.09
0612211042 ?3 16.75 78.(,1, 1. OR 35.17 78.5? 2641.0'I 2657.38 0.21069 536. 34 377.71 53.48 11.62
06/22/1043 23 19.75 '10.60 1. OB 41.50 ll'l.43 2424.92 2443.34 0.30457 775.30 462.76 n.11 9.14
06/ 22/ 1045 23 21.25 83.16 l. OB 44."66 83.36 2l'H.4'.l 2151.40 0.3A003 967.41 536.54 9:1.55 7.33
06/22/1046 123 11!. 25 87.51 1. 011 48.59 A7.51 18116. '11 1806.Bl 0.493'54 1256.37 640.51 132.63 5.61
0612211054 23 R.75 '19.35 - 1. 08 111. 31 9'1.55 li30.44 1121.67 0.10895 277.33 375.30 124 .• 25 6.20
06/2211055 23 11. 75 D'.l.24 1. 08 24.63 100.41 1093.04 1086.03 0.19861 505.59 508.46 173. 77 4.55 i-i
06/22/10'::6 23 14.75 l'.ll.27 ,l.'08 30.9-6 101.21 1051.75 1051.75 0.2'16",7 755.20 604.29 li3. 13 4.05 °' '°
TABLE XIII (Continued
DATE ·IIIW XLA TW TF T TEA VG VISW VIS8 HP QAGTT
06/22/1057 23 17.75 103.67 1.08 37.28 104.36 962.51 938.81 0.42785 1089.15
06/22/1059 23 20.45 101.10 1.08 42.98 109.81 850.66 800.70 0.59323 1510.12
AGPPH RER
723.63 285. 38
870.41 401.34
PN
3.41
2.12
I-' --:i 0
.APPENDIX E
ACCOUNTING FOR AXIAL HEAT. CONDUCTION IN .THE EXCHANGER
. WALL IN CALCULATING THE .EXPERIMENTAL HEAT
TRANSFER COEFFIC!ENT
Mathematical Devel9pment
The followlllg assumptions will be made:
(a) Radial temper~ture gradients can be neglected.
(b) The heat flux to the outside e:x:changerwall fromthe
electri~&l heating element is axially constant.
(c) The thermal conductivity is axially constant.
With .these assumptions a heat balance on an axial differential
element of the exchanger wall, wh;i.ch is shown schematically below, is
as follows:
171
172
After dividing through by Ac , allowing Ai:- to approach zero
and rearranging, the following relationship is obtained:
The heat flux from the electrical heating element (qH) has been
assumed axially constant; therefore, it can be obtained from the
electrical power measurements. P, Icwand Ac.(.)are lmown, thus it remains
only to calculate the second derivative of wall temperature with
respect to axial distance ~~ in order to obtain the heat flux
from the inner exchanger wall to the t'est fluid.
. oJZ.J'iv Before proceeding to calculating de z. , equation (E-2) will be
simplified by putting in lmown quantities.
Now
L = 22 inches
k = 116 Btu/hr ft F (for 6060 aluminum)
A = 2.718 square inches
P = 12.75 inches
With these substitutions equation (E-2) becomes:
= ) -1- f,t:Jlf: dZ,lw Q;.;. cl~ "Z-
(E-3)
o/zlte,) Calculation of c)~Z.. from Ex:perimental Wali Temperature Data:
Th t b . 'b'l't' f 1 lat' dz.Tw ere are wo o vious possi 1 l. ies or ca cu . ing cl c z.
.The first is to plot T vs. z on linear graph paper, obtain clh.l by . d~ using a straightedge, then plot j~ vs. z on linear graph paper and
then obtain ~~by using a straightedge. '.The second obvious.method
.is to use difference technique on the experimental temperatures. It is
173
also obvious that the difference technique can be applied to the
experimental data by.use of the digital comptJ.ter, whereas the g:raphical
technique cannot be done by digital computer.
Both technique~ have been used and compared on typic~l selected
data. The data selected for-the comparison were a series of runs for
. the 3 .500 inch diameter blade. Data for this blade were selected be-
cause the variation of heat transf~r coefficient with exohanger length
was probably greater in the laminar regime for this blade diameter than
any other blade diameter~ thus the correction for axial wall conduction
was greatest for the 3,500 inch diameter blade in the lam:inar :regim~.
The wall temperature profiles for the selected data are plotted ;in
Figure 32. The data. are in the creeping flow and lower. transition
. regimes. ~: which was obtained graphically is plotted vs. z in
Figores 33 and 34, -j;f which .was obtained graphd~~y is plotted
vs. z in Figure 35 .for one·half the selected runs. ~ de~ exhibits
large axial variations near the exchanger ends (0 to 6 inches and ·1$ to
22 inches) but relatively small axial variations in the exchanger
middle. For this.reason, calculations of heat transfer coefficients
near the exchanger ends. or performing any other calculations 'Which
would.involve using the second derivative near the end(:l would lack
sufficient accuracy to be helpful in interpreting the data or .in
determining the accuracy of the wall temperature profiles.
The inaccuracy.of the second derivative near.the ends. is of little
concern for this investigation because it is desired to obtain a local
heat transfer coefficient which is influenced as little as possible by
the exchanger ends. It appears from these data that the location
z = 14.inches might be the best axial location at whioh.to compute a
130
12
122
118
~114 ..
Q) 110 a .j.)
at i:., Q)
~106 Q) 8
,-; ,-; a:s ~ 102
98
94
N ()te: Day .of Tests
Tin:e of'
Test 1810
· 1830 1843 1915
was 03/29
2005 2040 2060 2110 2120 2130
174
1,36
132
128
124
120
104
100
90.t--'1!1~-~--o!!-5_---!!171"'"·.-~9~· --l~l~--~13~-~1"?'5-~1~7-·-... 1~9--2~1 ...... 96
Distance from Exchanger Inlet (inches), z
T vs .. z for Selected Tests with the 3.500 inch wDiameter Blade
175
Note: Day or Tests was 03/29
30
Time or
·Test Re 2040. 78
20 2060 113 2110 144
176 217
10
gT,u z o ...... ~~----~_..,..--,.~~~.,....----~~__..;~--~----~----......\.-11
<1!ch)
-10
-20
0 4 8 12 16 20
Distance from Exchange.r Inlet (inches) , z
Figure 33 • dTw vs/ z for. Selected Tests with the
rz 3.500 tnch Diameter alade
30 ·
20
(--L) inoh
-20
-30
b
Note: Day of Tests w.as 03/29
Time of Test · Re 1915 28
2005 48 .·
1843 16 1830 10 1810 '7 .4
4 8 12 ·.16 20
Distance.from Exchanger Inlet (inches), z
figure 34. dT vs. z for Selected Test$ with the ...;..J! .dz
3.500 inch Diameter Blade
176
80
2 a ~w dz
( F ) 1nch2
-2
-4
-6
Note: Day of Test_s was 05/29
'!'lme of
Test 2130
Re 217 7.4
28 113
(
-B~o ..... __ ._ __ _..,. __ _._ __ .-.!18 ............ ._ ... ~1~2------_.l_6 __ ...... ___ ·~20----'
.Distance from Excll:ilangeir Inlet ,(inches),, z
Figure 35. a2T vs. z for Selected 'T1est:s with the w
72""" dz
3.500 inch Diameter Blade
177
178
local heat transfer coefficient, the second derivative is nearly a.,,cially
constant at this location which should .be conducive to an accura.te
derivative; and the wall temperatuTe profiles peak in the laminar
regime near this ax.ial location which indicates that the heat transfer
coefficient may be affected the least by end effects at this loc1;).tion.
It should be noted that the axial location z = 14 inches is half-
way between wall temperatures T4 and T5. The second derivative was
calculated on the computer by taking the average of the numerically
calculated second derivativE?s at thermocouple locations 4 and 5. The
numerical calculation is as follows:
l;rJ;- 7j-~
Z0i!-)z..
(E-4)
It w.:1s found that this method of numerically calculating the
second de:civati.ve gave much more consistent results .than calcvlating
the second derivative numerically at a particular axial location at a
thermocouple; however 9 the average results were about the same when
compa.recl. on a plot of ~II vs. Re for a particular series of runs •
. The graphical second derivative at z = 14 inches and, the numer•i-
cally calculated second deriv--ative were both used to c{ioulate
(!~#)t-:Jf-. Table XIV presents a comparison.of ff~it')l-:/,-.
179
calculated by the two methods. The maximum deviation of the graphical
calculation from .the numerical calculation is 7. 5 percent for test
number 03/29/1843 and the other deviations are less; the average
absol~te deviation between the hand and numerical methods is 2.4 per~
cent.
This good comparison indicates that the numerically calculated
second derivative ts acceptable. This was the method used to obtain
. the local.heat transfer coefficient taking into account axial wall
conduction.
TABLE XIV
. COMPARISON OF GRAPHICAL AND NUMERICAL METHODS Of CALCULATING
qp/ qH AT z = 14 DJ CHES .FROM THE EXCBANGER INLET
.Time of
Test
1810
1830
1843
1915
2005
2040
2060
2110
2120
2130
Re
7.4
10.1
15.7
27J3
48.1
7$.6
113.5
144.4
176.9
218.8
qF/qH
Graphical NumertGal Method · Method
0.86 0.86
0.78 0.82
0,74 0.80
o. 73 0.75
o. 73 0.72
o. 71 0.70
o. 73 0.74
o. 73 0.76
1.12 L12
1.04 1.03
180
VITA
William Roy Penney
Candidate .for the Degree of
Doctor of Philosophy
.· Thesis: HEAT TRANSFER AND AGITATOR POWER REQUIREMENTS IN MECHANICALLY.,,. AGITATED THERMAL PROCESSORS WITH FIXED-CLEARANCE AGITATORS
Major Field: Chemical Thgineering
Biographical:
Personal Data: Born near Lockesburg, Arkansas, January 24, 1937, the son of Roy and Sally Mae Penney.
Education: Attended grade school at Falls Chapel and Ben Lorp.ond, Arkansas and high school at Ashdovm and W:j.nthrop, Arkansa:3; graduc1,ted from Winthrop High School in 1954; attended .Texarkana College, Texa.rkana, Texas for two years; transferred to the University of Arkansas at Fayetteville, Arkansas, received the Bachelor of Science degree in 1959 and the Master of Science degree in 1962, both with a major in Mechanical Thg:L""l.eering; attended Oklahoma State University from 1965 to 1968; completed the requirements for the Doctor of Philosophy
. degree i."'1. May, 1968.
Professional Experience: McDonnell Aircraft Company, St. Louis, Missouri, 1959 to 1960; Shell Chemical Company, Deer Park, Texas, Summer 1961; . Phillips Petroleum Company, Ba,rtlei:lville, Oklahoma, 1962 to 1965; Monsanto Company, Sto Louis, Missouri, since January, 1968.